Unit 1, Day 4 Worksheet

Unit 1, Day 4 Practice: Dilations & Combining

SOL Standard: AFDA.AF.1

Name: ___________________________________

Date: _______________

Worked Example

Describe all transformations for the equation $f(x) = 3(x-1)^2 + 4$

  1. Dilation: The '3' in front causes a vertical stretch (the graph will be skinnier).
  2. Horizontal Shift: The $(x-1)$ inside moves the graph right 1 unit.
  3. Vertical Shift: The $+4$ at the end moves the graph up 4 units.

Part 1: Describe All Transformations

For each equation, describe every transformation from the parent function.

1. $f(x) = 2x^2$

2. $f(x) = \frac{1}{3}x^2$

3. $f(x) = -4x^2$

4. $f(x) = 5x - 1$

5. $f(x) = 2(x-3)^2$

6. $f(x) = -(x+1)^2 + 6$

7. $f(x) = \frac{1}{2}(x-4)^2 + 1$

8. $f(x) = -3(x+2)^2$

Part 2: Write the Equation

Write the new equation based on the description.

9. The parent function $f(x)=x^2$ is stretched by a factor of 5.

10. The parent function $f(x)=x^2$ is compressed by a factor of $\frac{1}{4}$.

11. The parent function $f(x)=x$ is reflected over the x-axis and stretched by 2.

12. The parent function $f(x)=x^2$ is stretched by 3, moved right 2, and moved down 7.

Part 3: What's the Equation?

The dotted graph is the parent. Write the equation for the solid graph.

13. Equation for Graph A:

A

14. Equation for Graph B:

B

15. Equation for Graph C:

C