1. Section 3.1 Quadratic Functions

2. Graphs of Quadratic Functions

3. Graphs of Quadratic Functions Parabolas
Vertex
Minimum
Maximum
Axis of symmetry

5. Graphing Quadratic Functions in Standard Form
NOTE: I do not know why this book calls this the standard form when every other book calls it the “Vertex” form.

7. Seeing the Transformations

8. Using Standard Form
a<0 so parabola has a minimum, opens down

9. Example
Graph the quadratic function f(x) = - (x+2)2 + 4.

10. Example
Graph the quadratic function f(x) = (x-3)2 - 4

11. Graphing Quadratic Functions in the Form f(x)=ax2+bx+c

13. Using the form f(x)=ax2+bx+c
a>0 so parabola has a minimum, opens up

14. Example
Find the vertex of the function f(x)=-x2-3x+7

16. Example
Graph the function f(x)= - x2 - 3x Use the graph to identify the domain and range.

17. Minimum and Maximum Values of Quadratic Functions

19. Example
For the function f(x)= - 3x2 + 2x - 5
Without graphing determine whether it has a minimum or maximum and find it.
Identify the function’s domain and range.

20. Applications of Quadratic Functions

22. Example
You have 64 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

23. (a)
(b)
(c)
(d)

24. (a)
(b)
(c)
(d)