1. 9.4 Graphing Quadratics Three Forms

2. vertex standard factored
A quadratic equation can be written in three different forms: form, form, and form.
In order to graph each form, we need four key points and a key axis. The method to find these varies by form.
vertex
axis of symmetry
x-intercepts
y-intercept
vertex
standard
factored

3. Vertex Form upward downward
The vertex form of a quadratic equation is:
The graph the function is a parabola with vertex at . The parabola is symmetric with respect to the line If , the parabola opens ; if , the parabola opens .
upward
downward

4. Graph the parabola. 1. Find the vertex. Find the axis of symmetry.
Find the x-intercepts (let y=0)
Find the y-intercept (let x=0)

6. Graph the parabola. 2. Find the vertex. Find the axis of symmetry.
Find the x-intercepts (let y=0)
Find the y-intercept (let x=0)

8. Standard Form upward downward
The vertex form of a quadratic equation is:
The graph the function is a parabola with
vertex at The parabola is symmetric with respect to the line
. If , the parabola opens ; if , the parabola opens .
upward
downward

9. Graph the parabola. 3. Find the vertex. Find the axis of symmetry.
Find the x-intercepts (let y=0)
Find the y-intercept (let x=0)

11. Graph the parabola. 4. Find the vertex. Find the axis of symmetry.
Find the x-intercepts (let y=0)
Find the y-intercept (let x=0)

13. Factored Form upward downward
The vertex form of a quadratic equation is:
The graph the function is a parabola with
vertex at The parabola is symmetric with respect to the line
. If , the parabola opens ; if , the parabola opens .
upward
downward

14. Graph the parabola. 5. Find the vertex. Find the axis of symmetry.
Find the x-intercepts (let y=0)
Find the y-intercept (let x=0)

16. Graph the parabola. 6. Find the vertex. Find the axis of symmetry.
Find the x-intercepts (let y=0)
Find the y-intercept (let x=0)

18. Write the equation in vertex form.
7. The parabola has a vertex at and passes through the point

19. Write the equation in vertex form.
8. The parabola has a = 2, had x = -3 as its axis of symmetry, and passes through the point