Using the x-intercepts to Rewrite a Quadratic in Graphing Form

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# Using the x-intercepts to Rewrite a Quadratic in Graphing Form - PowerPoint PPT Presentation

Using the x-intercepts to Rewrite a Quadratic in Graphing Form. Graphing Form for a Parabola. y = a(x – h) 2 + k ( h, k ): The Vertex The value of a. same. opposite. Different Forms For a Quadratic. Same “ a ”. Parent Graph: y = x 2

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### Using the x-intercepts to Rewrite a Quadratic in Graphing Form

Graphing Form for a Parabola

y = a(x – h)2 + k

( h, k ):The Vertex

The value of a

same

opposite

Different Forms For a Quadratic

Same “a”

Parent Graph: y = x2

Factored Form: y = __( __x ± __ )( __x ± __)

Standard form: y = ax2 + bx + c

Graphing Form: y = a(x – h)2 + k

Same a!

Standard Form to Graphing Form: Factoring

Use an algebraic method to write in graphing form.

3. Average the x-intercepts for h

2

1. Find the value of a:

2. Find the x-intercepts

4. Substitute h into the rule for k

5. Substitute a, h, k into the graphing form

WARNING:

This method does not work if there are no x-intercepts

### Instead of Factoring, use the Quadratic Formula

Standard Form to Graphing Form: Quadratic Formula

Use an algebraic method to write in graphing form.

3. Average the x-intercepts for h

2

1. Find the value of a:

2. Find the x-intercepts

4. Substitute h into the rule for k

5. Substitute a, h, k into the graphing form

WARNING:

This method does not work if there are no x-intercepts