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

2. Table of Contents Pg Title Vocab Matching Activity LI/SC, Observations
Graphing Parabola Notes
LI/SC, Reflections
Graphing a(x – h)2

3. 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 -create a table of values to graph a function -graph data points from a table of values -find the y-intercept -find the vertex -find the axis of symmetry

4. 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

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

6. Reflection
How did “h” affect the shape of the parabola? How did “a” affect the shape of the parabola?

7. Reflection Answer Since h is positive, the parabola moves to the right
Since a is 1, the parabola’s width does not change

8. 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

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

10. Reflection
How did “h” affect the shape of the parabola? How did “a” affect the shape of the parabola?

11. Reflection Answer Since h is negative, the parabola moves to the left
Since a is 1, the parabola’s width does not change

12. Example 3: 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

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

14. Reflection
How did “h” affect the shape of the parabola? How did “a” affect the shape of the parabola?

15. Reflection Answer Since h is negative, the parabola moves to the left
Since a is 1/2, the parabola’s width becomes larger
Since a is negative, the parabola is upside down