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**9.4 Graphing Quadratics Three Forms**

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**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

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**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

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**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)

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**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)

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**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

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**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)

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**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)

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**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

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**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)

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**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)

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**Write the equation in vertex form.**

7. The parabola has a vertex at and passes through the point

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**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

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