Graphing Quadratic Functions – General Form

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

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

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

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

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

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

9. Vertex

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

11. x-intercepts

12. y-intercept

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

14. 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. END OF PRESENTATION Click to rerun the slideshow.