Question

Using the parent function y=x^2
, match the transformation with the correct equation.(5 points)
Horizontal shift, 5 units to the left
Vertical shift, 5 units up

Vertical shift, 5 units down

Horizontal shift, 5 units to the right

Vertical stretch, by a factor of 5

y = x^2 + 5

y = (x - 5)^2

y = (x + 5)^2

y = x^2 - 5

y = 5x^2

Answer 1

Here are the transformations matched with the correct equations based on the parent function \( y = x^2 \):

1. **Horizontal shift, 5 units to the left**:
- **Equation**: \( y = (x + 5)^2 \)

2. **Vertical shift, 5 units up**:
- **Equation**: \( y = x^2 + 5 \)

3. **Vertical shift, 5 units down**:
- **Equation**: \( y = x^2 - 5 \)

4. **Horizontal shift, 5 units to the right**:
- **Equation**: \( y = (x - 5)^2 \)

5. **Vertical stretch, by a factor of 5**:
- **Equation**: \( y = 5x^2 \)

So the matches are:
- **Horizontal shift, 5 units to the left**: \( y = (x + 5)^2 \)
- **Vertical shift, 5 units up**: \( y = x^2 + 5 \)
- **Vertical shift, 5 units down**: \( y = x^2 - 5 \)
- **Horizontal shift, 5 units to the right**: \( y = (x - 5)^2 \)
- **Vertical stretch, by a factor of 5**: \( y = 5x^2 \)