1. 4.5 Solving Quadratic Equations by Finding Square Roots

2. How would you solve the equation: x2 = 4 (take the square root of each side!)
* Remember, the square root of a positive # has 2 answers! (one + and one -)

3. Radical
Radical sign
Radicand

4. Properties of Square Roots
(a>0 and b>0)
Product Property –
Quotient Property-
Example:
Example:

5. Examples 1. 2. 3.

6. 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.

7. Can’t have a tent in the basement!
More Examples! 1. 2.
Can’t have a tent in the basement!

8. Conjugates
The product of 2 conjugates is always a rational number.

9. Rationalizing with Conjugates

10. Rationalizing with Conjugates34

11. Solving Quadratic Equations
Solve x2 = -9
-5x2 = -12
x2 =
Solve. 3(x-2)2=21
(x-2)2 = 7

12. More Examples!
4. Solve.
Solve. 4x2-6=42
+6 +6
4x2=48
x2 = 12

13. Falling Objects! Use h = -16t2 + h0
Height of the object after it has fallen
Object’s initial height
# of seconds after the object is dropped

14. 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?