1. Table of Contents 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. Table of Contents General Form of a Quadratic Function Standard Form of a Quadratic Function

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

4. Table of Contents Narrow Wide Plotting an Extra Point when Graphing Quadratics Choose a value for x 1 unit away from the vertex. Choose a value for x more than 1 unit away from the vertex

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

7. Table of Contents 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 a in 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. Table of Contents Summary for Graphing Quadratics in General Form Face Up Face Down Narrow Wide Vertex Axis of symmetry

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

10. Table of Contents Vertex

11. Table of Contents 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. Table of Contents Summary: Narrow Face down Axis: Point: Function:

13. Table of Contents 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. Table of Contents