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 Sketch the Graph of a Quadratic in Standard Form Face Up Face Down Vertex Axis of symmetry x-int: f (x) = 0 and solve for x y-int: x = 0 and solve for y Draw the parabola

4. Table of Contents Vertex - General Form Given the general form of a quadratic function … …the x-value of the vertex is given by

5. 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: To find the y-value of the vertex, just plug the x-value into the function …

6. 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 behavior, just as it did in the standard form.

7. Table of Contents Summary for Graphing Quadratics in General Form Face Up Face Down Axis of symmetry x-int: f (x) = 0 and solve for x y-int: x = 0 and solve for y

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

9. Table of Contents Vertex

10. Table of Contents Axis of Symmetry: x = x-value of vertex

11. Table of Contents x-intercepts

12. Table of Contents y-intercept

13. Table of Contents Summary: Face down Axis: Function: x-intercepts y-intercept

14. 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

15. Table of Contents