5.2 Solving Quadratic Equations Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve.
Download ReportTranscript 5.2 Solving Quadratic Equations Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve.
Slide 1
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 2
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 3
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 4
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 5
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 6
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 7
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 8
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 2
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 3
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 4
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 5
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 6
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 7
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54
Slide 8
5.2 Solving Quadratic Equations
Learning Objective: To solve quadratic equations by taking square roots and
to use the Pythagorean Theorem to solve problems involving right triangles.
Warm-up (IN)
CSAP Constructed Response
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Notes
Properties of Square roots
** Product property - ab a b
32 16 2 4 2
** Quotient property - a a
b
b
4
2
4
3
9
9
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 1 – Solve
a. 7 x 2 23 103
7 x 126
2
SADMEP!
x 18
x 9 2 3 2 or 4.24
2
b. 64x 5 289
2
289
x 5
64
17
x5
8
2
23
17
5
x
8
8
or
57
17
x 5 8
8
Try t his p. 282 (middle and bottom)
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 2 – A helicopter 85 ft above a designated area drops a
boxes of food to a disaster area. The height of the box
2
above the ground can be modeled by h t 16t 85 ,
where t is the time in seconds after it has been released.
After how many seconds will it hit the ground?
0 16t 2 85
85 16t
2
17
2
t
4
t 2.3sec
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
Pythagorean Theorem!
In a right , the sum of the squares of the lengths of the
legs is equal to the square of the hypotenuse.
a b c
2
2
2
c
a
b
EX 3 – Find the unknown length
8.4
a. A
B
5.3
b
C
2
b
8.4 5.3
2
b
28
.
09
70.56
2
98.65 b
2
9.93 b
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
b. J
k
1.9
K
2.8
L
1.9 k 2.8
3.61 k 2 7.84
k 2 4.23
k 2.06
2
2
2
Learning Objective: To solve quadratic equations by taking square roots and to use the
Pythagorean Theorem to solve problems involving right triangles.
EX 4 – What must be the length of QS so that it contacts
the ground halfway between the base of the tower and the
point where PS contacts the ground?
75 PR 2 1062
5626 PR 2 11236
PR 2 5611
1
QR PR
PR 74.91
2
2
S
106 ft
75 ft
2
SQ
37.45 75
5625 SQ2
83.83 ft SQ
2
P
Q
R
2
QR 37.45
Out – Describe the procedure you would use to
2
solve 5x 3 12
Summary – So, I was
thinking…
POW!!
HW – p. 287
#21-43 odd,
51-54