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

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Presentation transcript:

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

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

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

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???

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

Checkpoint Simplify the expression. 1. Use Properties of Square Roots ANSWER

Example 3 Solve a Quadratic Equation Solve. = x 2x Subtract 1 from each side. = 12x 2x 2 SOLUTION = x 2x 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 –

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

Checkpoint Solve the equation. Solving a Quadratic Equation 4. = x 2x 2 4 – = x 2x ANSWER 2,2, 3 23 – 10, 10 – = 3y 23y ANSWER 2,2, 2 22 –

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