1.  FIND THE VERTEX, THE AXIS OF SYMMETRY, AND THE MAXIMUM OR MINIMUM VALUE OF A QUADRATIC FUNCTION USING THE METHOD OF COMPLETING THE SQUARE.  GRAPH QUADRATIC FUNCTIONS.  SOLVE APPLIED PROBLEMS INVOLVING MAXIMUM AND MINIMUM FUNCTION VALUES. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley 3.3 Analyzing Graphs of Quadratic Functions

2. Quadratic Functions: f (x) = a(x  h) 2 + k Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley The graph of a quadratic function is called a parabola.

3. Examples Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley For the functions: a ) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) On what intervals is the function increasing? decreasing?

4. Example Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Find the vertex by writing the function in standard form. Then find the axis of symmetry, and the maximum or minimum value of f (x) = x 2 + 10x + 23. Then graph the function.

5. Vertex of a Parabola Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley The vertex of the graph of f (x) = ax 2 + bx + c is We calculate the x-coordinate. We substitute to find the y-coordinate.

6. Example Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley For the functions: a) Find the vertex. b) Determine whether there is a maximum or minimum value and find that value. c) Find the range. d) On what intervals is the function increasing? decreasing?

7. Application - Example Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley A stonemason has enough stones to enclose a rectangular patio with 60 ft of stone wall. If the house forms one side of the rectangle, what is the maximum area that the mason can enclose? What should the dimensions of the patio be in order to yield this area?

8. Application Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

9. Example Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley