Unit 1, Day 4 Practice: Dilations & Combining
SOL Standard: AFDA.AF.1
Name: ___________________________________
Date: _______________
Worked Example
Describe all transformations for the equation $f(x) = 3(x-1)^2 + 4$
- Dilation: The '3' in front causes a vertical stretch (the graph will be skinnier).
- Horizontal Shift: The $(x-1)$ inside moves the graph right 1 unit.
- 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:
14. Equation for Graph B:
15. Equation for Graph C: