 # 9.4 Graphing Quadratics Three Forms

## Presentation on theme: "9.4 Graphing Quadratics Three Forms"— Presentation transcript:

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

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

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)

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)

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

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)

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)

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

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)

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)

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

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