1. Quadratic Functions: f(x) = a(x – h)2

2. Table of Contents
46: Warm-Up
47: How Do I Graph an Equation in the Form a(x – h)2?

3. Warm-Up
Explain how the graph f(x) = x2 will be transformed for each of the following P(x) = -x2 + 50
2. C(x) = -3x2
3. K(x) = ½x2 – 16

4. Pop Quiz
Each of the following parabolas represents a quadratic function for the form f(x) = ax2 + c. For each parabola, circle whether the values for “a” and “c” are positive, negative, or zero.

5. Learning Intention/Success Criteria
LI: We are learning how to graph parabolic functions in the form a(x – h)2 SC: I know how to -recognize if a quadratic function opens upwards or downwards -graph parabolic functions -use a table of values to graph a function -find the y-intercept -

6. EQ: How Do I Graph an Equation in the Form a(x – h)2?
5/22/2019

7. Vertex
The point where the parabola makes its sharpest turn
Maximum Vertex
The highest point in a parabola
Only true when A is negative
Minimum Vertex
The lowest point in a parabola
Only true when A is positive

8. Roots
The solution to an equation in the form f(x) = 0.
Where the line crosses the x-axis
Called zeroes or x-intercepts

9. Example 1: Create a table and graph the function, as compared to the parent function
f(x) = (x – 1)2 x
Work
f(x) -2
(-2 – 1)2
= (-3)2 9 -1
(-1 – 1)2
= (-2)2 4
(0 – 1)2
= (-1)2 1 1
(1 – 1)2
= (0)2 2
(2 – 1)2
= (1)2 1 3
(3 – 1)2
= (2)2 4 4
(4 – 1)2
= (3)2 9

10. x
f(x) -2 9 -1 4 1 2 3
Vertex:
(1, 0)
x = 1
Axis of Symmetry:

11. Example 2: Create a table and graph the function, as compared to the parent function
f(x) = (x + 2)2 x
Work
f(x) -5
(-5 + 2)2
= (-3)2 9 -4
(-4 +2)2
= (-2)2 4 -3
(-3 + 2)2
= (-1)2 1 -2
(-2 + 2)2
= (0)2 -1
(-1 + 2)2
= (1)2 1
(0 + 2)2
= (2)2 4 1
(1 + 2)2
= (3)2 9

12. x
f(x) -5 9 -4 4 -3 1 -2 -1
Vertex:
(-2, 0)
x = -2
Axis of Symmetry:

13. Example 3: Create a table and graph the function, as compared to the parent function
f(x) = 2(x – 1)2 x
Work
f(x) -2
2(-2 – 1)2
= 2(-3)2 18 -1
2(-1 – 1)2
= 2(-2)2 8
2(0 – 1)2
= 2(-1)2 2 1
2(1 – 1)2
= 2(0)2 2
2(2 – 1)2
= 2(1)2 2 3
2(3 – 1)2
= 2(2)2 8 4
2(4 – 1)2
= 2(3)2 18

14. x
f(x) -2 18 -1 8 2 1 3 4
Vertex:
(1, 0)
x = 1
Axis of Symmetry:

15. Example 4: Create a table and graph the function, as compared to the parent function
f(x) = -½(x + 2)2 x
Work
f(x) -8
-½(-8 + 2)2
= -½(-6)2
-18 -6
-½(-6 + 2)2
= -½(-4)2 -8 -4
-½(-4 + 2)2
= -½(-2)2 -2 -2
-½(-2 + 2)2
= -½(0)2
-½(0 + 2)2
= -½(2)2 -2 2
-½(2 + 2)2
= -½(4)2 -8 4
-½(4 + 2)2
= -½(6)2
-18

16. x
f(x) -8
-18 -6 -4 -2 2 4
Vertex:
(-2, 0)
x = -2
Axis of Symmetry: