Transcript 1.5 Solving Quadratic Equations by Finding Square Roots

1.5
Solving Quadratic Equations
by Finding Square Roots
(p. 32)
How do you simplify radicals?
What are the steps to rationalize a denominator?
What is a conjugate?
How many answers will you get when you solve a
quadratic equation by finding square roots?
Identify the formula h = −16t2 + h0?
How would you solve the equation:
x2 = 4
(take the square root of each side!)
x 4
2
x  4
x  2 or - 2 *
2
* Remember, the square
root of a positive # has
2 answers! (one + and
one -)
Radical
3
Radical
sign
Radicand
Properties of Square Roots
(a>0 and b>0)
1. Product Property –
2. Quotient Property-
ab  a * b
a
a

b
b
Example:
40  4 *10  4 * 10  2 10
Example:
3
3
3


4
2
4
Examples
1.
2.
500  100 * 5  100 * 5
 10 5
3 12 * 6  3 12 * 6  3 72  3 36 * 2
 3 * 6 2  18 2
3.
25
9
25

9
5

3
Rationalizing the Denominator
You CANNOT leave a radical in the
denominator of a fraction!
No tents in the basement!!!!
(the numerator is OK)
Just multiply the top & bottom of the fraction
by the radical to “rationalize” the
denominator.
More Examples!
1.
25
3
25

3

5 * 3
3 * 3

5 3
9

5 3
3
Can’t have a tent in the
basement!
2.
2
11
2

11
* 11
22

* 11
121
22

11
Conjugates
•
Rationalize the denominator of fractions
SOLUTION
Guided Practice
Solving Quadratic Equations
1. Solve. 3 - 5x2 = -9
-3
-3
-5x2 = -12
-5
-5
x2 = 12
5
12
x 
5
2
2. Solve. 3(x-2)2=21
3
3
(x-2)2 = 7
( x  2) 2   7
x2   7
x  2 7
12
12 * 5
60
4 *15  2 15
x




5
5
5
5*5
25
More Examples!
3. Solve.
4x2-6=42
+6 +6
4x2=48
4
4
x2 = 12
x 2   12
x   4 * 3  2 3
4. Solve.
1
( x  4) 2  6
5
( x  4) 2  30
( x  4) 2   30
x  4   30
x  4  30
Falling Objects!
• Use h = -16t2 + h0
Height
of the
object
after it
has
fallen
# of seconds
after the
object is
dropped
Object’s
initial
height
Example
• The tallest building in
the USA is in
Chicago, Illinois. It is
1450 ft. tall. How
long would it take a
penny to drop from
the top of the building
to the ground?
h  16t  h0
2
0  16t  1450
2
 1450  16t
90.625  t
2
2
90.625  t 2
t  9.52 seconds
• How do you simplify radicals?
• What are the steps to rationalize a
denominator?
• What is a conjugate?
• How many answers will you get when you
solve a quadratic equation by finding
square roots?
• Identify the formula h = −16t2 + h0?
Assignment
p. 35, 4-18 even,
22-32 even, 38, 39