534 Chapter 9Solving Quadratic Equations9
9
Chapter ReviewProperties of Radicals (pp. 479–488)9.1a. Simplify 3 √— 27x10 .3 √— 27x10 3 √—
27 ⋅ x9 ⋅ x Factor using the greatest perfect cube factors. 3 √— 27 ⋅ 3 √— x9 ⋅ 3 √— x Product Property of Cube Roots 3x3 3 √— x Simplify.b.Simplify 12 — 3 √— 5 .12 — 3 + √— 5 12 — 3 + √— 5 ⋅ 3 √— 5 — 3 √— 5 The conjugate of 3 + √— 5 is 3 √— 5 . 12 ( 3 √— 5 )
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32 ( √— 5 ) 2 Sum and difference pattern 36 12 √— 5
— 4 Simplify. 9 3 √— 5 Simplify.Simplify the expression.1. √— 72p7 2. — 45 — 7y 3. 3 — 125x11 — 4 4. 8 — √— 6 + 2 5. 4 √— 3 + 5 √— 12 6. 15 3 √— 2 2 3 √— 54 7. ( 3 √— 7 + 5 ) 2 8. √— 6 ( √— 18 + √— 8 ) Solving Quadratic Equations by Graphing (pp. 489–496)9.2Solve x2 3x = 4 by graphing.Step 1 Write the equation in standard form. x2 + 3x 4 Write original equation. x2 + 3x 4 0 Subtract 4 from each side.Step 2 Graph the related function y x2 + 3x 4.Step 3Find the x-intercepts. The x-intercepts are 4 and 1. So, the solutions are x 4 and x 1.Solve the equation by graphing.9. x2 9x + 18 0 10. x2 2x 4 11. 8x 16 x2 12. The graph of f (x) (x + 1)(x2 + 2x 3) is shown. Find the zeros of f. 13. Graph f (x) x2 + 2x 5. Approximate the zeros of f to the nearest tenth.4212x25yy x2 + 3x 4242xy4244f(x) (x + 1)(x2 + 2x 3)Dynamic Solutionsavailable at BigIdeasMath.com