1. Table of Contents Graphing Quadratic Functions – Standard Form It is assumed that you have already viewed the previous slide show titled Graphing Quadratic Functions – Concept. The summary of the Concept slide show is given again on the next page.

2. Table of Contents SUMMARY Axis of symmetry: Graphs of Quadratic Functions The graph of a quadratic function in called a parabola. The maximum or minimum y-value of a quadratic occurs at the vertex. Face UpFace Down x-int: y = f (x) = 0 and solve for x. y-int: x = 0 and solve for y.

3. Table of Contents The vertex is given by V(h,k). Example 1 The vertex is given by: A quadratic function in what we will call Standard Form is given by:

4. Table of Contents Example 2 The vertex is given by: Put the function in the form of …

5. Table of Contents The vertex is given by: Here is an easier way to work the last problem: For the h value, take the opposite sign … For the k value, take the same sign …

6. Table of Contents Example 3 The vertex is given by:

7. Table of Contents Recall that the Axis of Symmetry has the equation Since the vertex of the standard quadratic function given by has an x-value of h, we can write the equation of the axis of symmetry as Put all of the tools learned so far together to sketch the graph of a quadratic function in standard form.

8. 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

9. Table of Contents Example 4 Sketch the graph of the following function:

10. Table of Contents Start the sketch of the graph with what we have so far. The parabola is face up

11. Table of Contents x-intercepts y-intercept

12. Table of Contents Plot the intercepts x-intercepts y-intercept

13. Table of Contents Sketch the parabola, using the points and axis of symmetry.

14. Table of Contents Example 5 Sketch the graph of the following function:

15. Table of Contents Start the sketch of the graph with what we have so far. The parabola is face down

16. Table of Contents x-intercepts

17. Table of Contents Plot the x-intercepts x-intercepts

18. Table of Contents y-intercept

19. Table of Contents Skip plotting the y-intercept since it is off of the graph. Sketch the parabola, using the points and axis of symmetry.

20. Table of Contents