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Graphing Quadratic Functions – General Form

Graphing Quadratic Functions – General Form. It is assumed that you have already viewed the previous three slide shows titled Graphing Quadratic Functions – Concept Graphing Quadratic Functions – Standard Form Graphing Quadratic Functions – Converting General Form To Standard Form.

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Graphing Quadratic Functions – General Form

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  1. Graphing Quadratic Functions – General Form • It is assumed that you have already viewed the previous three slide shows titled • Graphing Quadratic Functions – Concept • Graphing Quadratic Functions – Standard Form • Graphing Quadratic Functions – Converting General Form To Standard Form • The next three pages are summaries from those shows, and are important to understanding this module.

  2. Standard Form of a Quadratic Function General Form of a Quadratic Function

  3. Graphing a Quadratic Function in Standard Form Vertex Face Up Face Down Axis of symmetry Narrow Wide

  4. Wide Narrow Plotting an Extra Point when Graphing Quadratics Choose a value for x1 unit away from the vertex. Choose a value for xmore than 1 unit away from the vertex

  5. Vertex of the Graph of a Quadratic Function in General Form • Given the general form of a quadratic function … …the x-value of the vertex is given by

  6. There are two other helpful concepts for graphing a quadratic function that is in general form. • Concept 1: We already know that the x-value of the vertex is given by … The y-value of the vertex is given by …

  7. Thus, the vertex of the graph of the quadratic function in general form is given by • Concept 2: The a of the general form is the same value as the a in the standard form. This means that the ain the general form can be used to determine the face up/face down and narrow/wide behavior, just as it did in the standard form.

  8. Summary for Graphing Quadratics in General Form Vertex Face Up Face Down Narrow Axis of symmetry Wide

  9. Example: Sketch the graph of the given quadratic function. Face down Narrow Vertex:

  10. Vertex

  11. Axis of Symmetry: x = x-value of vertex Point: since the parabola is narrow, use an x-value that is only one unit from the vertex.

  12. Function: Axis: Point: Summary: Face down Narrow

  13. Plot the vertex Plot the axis: Plot the point: Draw the branch of the parabola on the right side of the axis. Use symmetry to draw the left branch. Label

  14. END OF PRESENTATION

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