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

This guide explains how to rewrite a quadratic function into graphing form using its x-intercepts. Start with the standard form of the quadratic equation, identify the x-intercepts, and calculate the vertex coordinates. Learn how to find the coefficient "a" consistently across different forms of the quadratic and understand that this method requires x-intercepts. If intercepts are absent, the quadratic formula serves as an alternative. Follow the steps outlined for accurate graphing of parabolas.

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

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

  2. Graphing Form for a Parabola y = a(x – h)2 + k ( h, k ):The Vertex The value of a same opposite

  3. 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

  4. Justification that the “a” in Standard and Graphing Form are the same Same a!

  5. 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

  6. Instead of Factoring, use the Quadratic Formula

  7. 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

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