#### 5.2 Solving Quadratic Equations Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve.

download report#### Transcript 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