1. 4.5
Solving Quadratic Equations
by Finding Square Roots
(p. 250-253)

2. 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 -)

3. Radical
3
Radical
sign
Radicand

4. 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

5. 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

6. Rationalizing the Denominator
You CANNOT leave a radical in the
denominator of a fraction!
(the numerator is OK)
Just multiply the top & bottom of the fraction
by the radical to “rationalize” the
denominator.

7. 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

8. 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

9. More Examples!
3. Solve. 4x -6=42
+6 +6
4x2=48
4
4
x2 = 12
x 2 = ± 12
2
x = ± 4 * 3 = ±2 3
1
5
4. Solve. ( x − 4) 2 = 6
( x − 4) 2 = 30
( x − 4) 2 = ± 30
x − 4 = ± 30
x = 4 ± 30

10. 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

11. 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 2 + h0
0 = −16t + 1450
2
− 1450 = −16t
90.625 = t
2
2
90.625 = t 2
t ≈ 9.52 seconds