1. Quadratic Functions and Their Graph
Section 11.6
Quadratic Functions and Their Graph

2. Basic Graph
Graph y = f(x) = x²

3. Complex Quadratic Equation
The complex quadratic equation has the form
y = f(x) = ± a(x – h)² + k
The ±, a, h, and k change the basic graph to create the new complex graph.

4. Complex Quadratic Equation
The complex quadratic equation has the form
y = f(x) = ± a(x – h)² + k
Determines the direction the parabola is facing
+ graph open upward
– graph opens downward

5. The difference between the + and -

6. Complex Quadratic Equation
The complex quadratic equation has the form
y = f(x) = ± a(x – h)² + k a
Determines the width of the graph based on the basic graph y = f(x) = x²
0<a<1 wide graph
a>1 narrow graph

7. a
When the a changes the width of the graph changes.

8. Complex Quadratic Equation
The complex quadratic equation has the form
y = f(x) = ± a(x – h)² + k h
Indicates how much the graph will be moving along the x – axis, the horizontal movement
+h moves to the right h units
-h moves to the left h units

9. h
What happens when we have a h

10. Complex Quadratic Equation
The complex quadratic equation has the form
y = f(x) = ± a(x – h)² + k k
Indicates how much the graph will be moving along the y-axis, the vertical movement.
+k move up k units
-k move down k units

11. k
What happens with a k

12. Vertex
Vertex
Lowest point (minimum) or the highest point (maximum) of a graph
You will have a lowest point if the sign is +
You will have a highest point if the sign is -
Algebraically defined by the point (h,k)
Find the vertex, then determine if the point is a max or min y = -2(x + 3)² - 1

13. Graph Example
Graph y = -x² - 3

14. Graph Example
Graph f(x) = 2(x + 3)²

15. Graph Example
Graph f(x) = -3(x – 2)² +1

16. Graph Example
Graph y = ½(x - 2)² - 3

17. Homework
Section 11.6
#9, 11, 15, 17,35, 37, 39, 41, 43, 45