Warm Up 1. Graph y = x2 + 4x + 3. 2. Identify the vertex and zeros of the function above. vertex:(–2 , –1); zeros:–3, –1

Objective Solve quadratic equations by graphing.

Every quadratic function has a related quadratic equation 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

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.

Solve the equation by graphing the related function. 2x2 – 18 = 0 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.

Solve the equation by graphing the related function. –12x + 18 = –2x2 The axis of symmetry is x = 3. The vertex is (3, 0). The y-intercept is 18.

Solve the equation by graphing the related function. x2 – 8x – 16 = 2x2 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.

A frog jumps straight up from the ground 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? pp. 625-627/15-29,31,37-43 Odd,49-61 Odd