1. 5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012

2. Properties of Square Roots Product Property Ex: Quotient Property Ex:

3. Example 1 Use Properties of Square Roots Simplify the expression. a. 18 b. 2 10 c. 9 5 SOLUTION 9 a. 18 = 2 = 2 3 c. 9 5 5 9 == 5 3 4 b. = = 5 2 1020 = 5 2

4. Simplifying Fractions with √ in denominator. You must eliminate any radicals in the denominator. By multiplying the numerator and denominator by That’s the same as multiplying by 1 which doesn’t change the value of the fraction. How???

5. Example 2 Rationalize the Denominator of a Fraction Simplify. 2 5 SOLUTION 2 5 5 2 = Quotient property of square roots 5 2 = 2 2 2 2 Multiply by. = 10 2 Simplify.

6. Checkpoint Simplify the expression. 1. Use Properties of Square Roots 12 2. 3 15 3. 3 7 ANSWER 3 2 5 3 21 3

7. Example 3 Solve a Quadratic Equation Solve. = x 2x 2 +113 Subtract 1 from each side. = 12x 2x 2 SOLUTION = x 2x 2 +113 Write original equation. = x + – 12 Take the square root of each side. = x + – 43 Product property of square roots = x + – 32 Simplify. ANSWER The solutions are and. 32 32 –

8. Example 3 Solve a Quadratic Equation CHECK 32 32 – Substitute and into the original equation. = x 2x 2 +113 = x 2x 2 +1 +1 = ? 43 +113 = ? 43 = 12+113 = 12+113 +1 32()2)2 = ? +1 = ? 32()2)2 –

9. Checkpoint Solve the equation. Solving a Quadratic Equation 4. = x 2x 2 4 – 14 5. = x 2x 2 313+ ANSWER 2,2, 3 23 – 10, 10 – = 3y 23y 2 24 6. ANSWER 2,2, 2 22 –

10. Homework 5.6 p.258 #18-21, 30-33, 38-41, 50-53