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Do Now 4/15/10

Do Now 4/15/10. Take out HW from yesterday. Practice worksheet 10.2 form B odds Copy HW in your planner. Text p. 647, #8, 14, 17, 24, 30 Quiz sections 10.1-10.3 Monday. 1) a = 6, b = 3, c = 5 3) a = 7, b = -3, c = -1 5) a = 3/4, b = 0, c = -10 7) up; x = 0; (0,-5)

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Do Now 4/15/10

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  1. Do Now 4/15/10 • Take out HW from yesterday. • Practice worksheet 10.2 form B odds • Copy HW in your planner. • Text p. 647, #8, 14, 17, 24, 30 • Quiz sections 10.1-10.3 Monday.

  2. 1) a = 6, b = 3, c = 5 3) a = 7, b = -3, c = -1 5) a = 3/4, b = 0, c = -10 7) up; x = 0; (0,-5) 9) down; x = 3/2; (3/2, 23/2) 11) up; x = -1; (-1, -5) 13) up; x = -5; (-5, -33/2) 15) down; x = 3/2; (3/2, -5/4) 17) down; x = 7/4; (7/4, 57/8) 19) 21) 23-31) on overhead 33) maximum; (1,3) 35) 12 ft Homework Practice 10.2 Form B odds

  3. Objective • SWBAT solve quadratic equations by graphing

  4. Section 10.3 “Solve Quadratic Equations by Graphing” QUADRATIC EQUATION- an equation that is in the standard form ax² + bx + c = 0, where a = 0. Solve by Factoring (Chapter 9) Solve by Graphing y x² - 6x + 5 = 0 x x² - 6x + 5 = 0 (x – 1)(x – 5) = 0 x = 1 or x = 5 To solve this equation graph y = x² - 6x + 5. From the graph you can see that the intercepts are 1 and 5. (Remember This???)

  5. Solving Quadratic Equations by Graphing To solve a quadratic equation by graphing, first write the equation in standard form, ax² + bx + c = 0. Then graph the equation. The x-intercepts of the graph are the solutions, or roots, of the equation. Quadratic equations can have one of three types of solutions: • Two solutions (2) One solution (3) No solution y y y x x x One x-intercept No x-intercepts Two x-intercepts

  6. EXAMPLE 1 Solve a quadratic equation having two solutions Solvex2 – 2x = 3by graphing. SOLUTION STEP 1 Write the equation in standard form. x2 – 2x = 3 Write original equation. x2 – 2x – 3 = 0 Subtract 3 from each side. STEP 2 Graph the functiony = x2 – 2x – 3. Thex-intercepts are – 1 and 3

  7. ANSWER The solutions of the equationx2 – 2x = 3are– 1and3. (3)2 –2(3) 3 (–1)2 –2(–1) 3 3 = 3 3 = 3 ? ? = = EXAMPLE 1 Solve a quadratic equation having two solutions CHECK: You can check – 1 and 3 in the original equation. x2 – 2x = 3 x2 – 2x = 3 Write original equation. Substitute for x. Simplify. Each solution checks.

  8. EXAMPLE 2 Solve a quadratic equation having one solution Solve – x2 + 2x = 1 by graphing. SOLUTION STEP 1 Write the equation in standard form. – x2 + 2x = 1 Write original equation. – x2 + 2x – 1 = 0 Subtract 1 from each side. STEP 2 Graph the functiony = – x2 + 2x – 1. The x-intercept is 1.

  9. EXAMPLE 3 Solve a quadratic equation having no solution Solve x2 + 7 = 4xby graphing. SOLUTION STEP 1 Write the equation in standard form. x2 + 7 = 4x Write original equation. x2 – 4x + 7 = 0 Subtract 4xfrom each side. STEP 2 Graph the function y = x2 – 4x + 7. The equation x² + 7 = 4xhas no solution because there is no x-intercept.

  10. f(–7) = (–7)2 + 6(– 7) – 7 = 0 f(1) = (1)2+ 6(1) – 7 = 0 ANSWER The zeros of the function are – 7and 1. EXAMPLE 4 Find the zeros of a quadratic function Find the zeros of f(x) = x2 + 6x – 7. SOLUTION Graph the function f(x) = x2 + 6x –7. The x-intercepts are – 7 and 1. CHECK Substitute – 7 and 1 in the original function.

  11. Homework • Text p. 647, #8, 14, 17, 24, 30

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