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9. 5 Solving Quadratic Equations by Graphing ESTIMATING SOLUTIONS BY GRAPHING The solutions of a quadratic equation in one variable x can be estimated by graphing. Use the following steps: STEP 1 Write the equation in the standard for ax 2 +bx + c = 0 STEP 2 Sketch the graph of the related quadratic function y = ax 2 +bx + c STEP 3 Estimate the values of the x-intercepts, if any. The solutions, or roots, of ax 2 +bx + c = 0 are the x-intercepts of the graph.

9. 5 Solving Quadratic Equations by Graphing Solve an Equation by Graphing 1. x 2 + 2 x = 3 x -3 -2 -1 0 1 y 0 -3 -4 -3 0 (-3, 0) x-intercept (1, 0) x-intercept y = x 2 + 2 x - 3

9. 5 Solving Quadratic Equations by Graphing Solve an Equation by Graphing 2. x 2 - x = 12 x -3 -2 -1 0 yy 0 -6 -10 -12. 25 1 2 3 4 -12 -10 -6 0 In order to fit all of the function on the graph, you must scale the y’s by 2. (+20 at top, -20 at bottom. ) (-3, 0) x-intercept y = x 2 - x - 12 (4, 0) x-intercept

9. 5 Solving Quadratic Equations by Graphing Solve an Equation by Graphing 3. -4 x 2 - 8 x = -12 x -3 -2 -1 0 1 y 0 12 16 12 0 y = -4 x 2 - 8 x + 12 In order to fit all of the function on the graph, you must scale the y’s by 2. (+20 at top, -20 at bottom. ) (-3, 0) x-intercept (1, 0) x-intercept