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

2. Learning Target
Students will be able to: Solve quadratic equations by graphing.

3. 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

4. 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.

5. 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.

6. 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.

7. 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.

8. 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 /15-29,31,37-43 Odd,49-61 Odd