1. Graphing Quadratic Equations
Section 9.4
Graphing Quadratic Equations

2. Example Graph the equation y = x2 by plotting points. y x y x 2 4 13 4 1 2 3 4 y x 2 4 1 1 1 1 2 4 2

3. Example Graph the equation y = x2 by plotting points. y x y x 2 41 2 3 4 1 2 3 4 y x 2 4 1 1 1 1 2 4 3

4. Graphs of Quadratic Equations
The graph of the quadratic equation y = ax2 + bx + c is a parabola. The vertex is the lowest point on a parabola that opens upward or the highest point on a parabola that opens downward. x y 1 2 3 4 1 2 3 4
vertex
vertex 4

5. Vertex of a Parabola Vertex of a Parabola
The x-coordinate of the vertex of the parabola described by y = ax2 + bx + c is 5

6. Example Determine the vertex of y = 3x2 + 6x – 7. y = 3x2 + 6x – 7
= 3(1)2 + 6(1)  7
= 3  6  7
(1, ?)
= 10
The vertex is (–1, –10). 6

7. Example
Determine the vertex and x-intercepts of y = –2x2 – 8x + 4 and sketch the graph.
y = –2x2 – 8x + 4
= –2(2)2 – 8(2) + 4
= –2(4)
= 12
The vertex is (–2, 12).
Continued 7

8. Example (cont)
Determine the vertex and x-intercepts of y = –2x2 – 8x + 4 and sketch the graph.
The x-intercepts occur where y = 0. x y 2 4 6 8 2 4 6 8
12
16 12 16
–2x2 – 8x + 4 = 0
vertex
Use the quadratic formula to determine the x-intercepts.
x =  x = 0.4 8