2. 5.3 Solving Quadratic Equations by Finding Square Roots Goals: 1. Solve quadratic equations by finding square roots 2. using quadratic models in real life For what purpose would you use the product or quotient properties of square roots when solving quadratic equations using square roots?

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

4. Radical Radical sign Radicand

5. Properties of Square Roots (a>0 and b>0) 1.Product Property – 2.Quotient Property- Example: Example:

6. Examples 1. 2. 3.

7. Rationalizing the Denominator You CANNOT leave a radical in the denominator of a fraction! Just multiply the top & bottom of the fraction by the radical to “rationalize” the denominator.

8. Examples 1. 2. Can’t have a radical in the denominator!

9. Solving Quadratic Equations 1.Solve. 3 - 5x 2 = -9 -3 -3 -5x 2 = -12 -5 -5 x 2 = 2. 2.Solve. 3(x-2) 2 =21 3 3 (x-2) 2 = 7

10. More Examples! 3.Solve. 4x 2 -6=42 +6 +6 4x 2 =48 4 4 x 2 = 12 4. Solve.

11. Falling Objects! Use h = -16t 2 + h 0 Height of the object after it has fallen # of seconds after the object is dropped Object’s initial height

12. 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?