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Solving Quadratic Equations 9-5 by Graphing Warm Up 1. Graph y = x2 + 4x + 3. 2. Identify the vertex and zeros of the function above. vertex:(–2 , –1); zeros:–3, –1 Holt Algebra 1 Solving Quadratic Equations 9-5 by Graphing Objective Solve quadratic equations by graphing. Holt Algebra 1 Solving Quadratic Equations 9-5 by Graphing Every quadratic function has a related quadratic equation. A quadratic equation is an equation that can be written in the standard form ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. When writing a quadratic function as its related quadratic equation, you replace y with 0. So y = 0. y = ax2 + bx + c 0 = ax2 + bx + c ax2 + bx + c = 0 Holt Algebra 1 Solving Quadratic Equations 9-5 by Graphing One way to solve a quadratic equation in standard form is to graph the related function and find the x-values where y = 0. In other words, find the zeros of the related function. Recall that a quadratic function may have two, one, or no zeros. Holt Algebra 1 Solving Quadratic Equations 9-5 by Graphing Solve the equation by graphing the related function. 2 2 2x – 18 = 0 y 2 x 18 • The axis of symmetry is x = 0. • The vertex is (0, –18). • Two other points (2, –10) and (3, 0) • Graph the points and reflect them across the axis of symmetry. The zeros appear to be 3 and –3. Holt Algebra 1 3 3,0 2, 10 Solving Quadratic Equations 9-5 by Graphing Solve the equation by graphing the related function. –12x + 18 = –2x2 2 x 2 12 x 18 0 • The axis of symmetry is x = 3. • The vertex is (3, 0). • The y-intercept is 18. x 3 Holt Algebra 1 6 Solving Quadratic Equations 9-5 by Graphing Solve the equation by graphing the related function. x2 – 8x – 16 = 2x2 y x 8 x 16 • The axis of symmetry is x = –4. • The vertex is (–4, 0). • The y-intercept is 16. • Two other points are (–3, 1) and (–2, 4). • Graph the points and reflect them across the axis of symmetry. The only zero appears to be –4. Holt Algebra 1 2 0,16 4 2 Solving Quadratic Equations 9-5 by Graphing A frog jumps straight up from the ground. The quadratic function f(t) = –16t2 + 12t models the frog’s height above the ground after t seconds. About how long is the frog in the air? 0 16t 12t 2 0.75 seconds 0 4t 4t 3 4t 0 or 4t 3 0 3 t 0 or t 4 pp. 625-627/15-29,31,37-43 Odd,49-61 Odd Holt Algebra 1 1 4