Question

Use the parent function: y = x^2, match the transformation with the correct equation.
1. Vertical shift, four units up.
2. Horizontal shift, 4 units to the right.
3. Horizontal shift, 4 units to the left.
4. Vertical shift, 4 units down.
Equations:
A. y = (x + 4)^2
B. y = (x - 4)^2
C. y = x^2 - 4
D. y = x^2 + 4

Answer 1

Let's match each transformation with the correct equation based on the parent function \( y = x^2 \).

1. **Vertical shift, four units up.**
Equation: **D. \( y = x^2 + 4 \)**
(This shifts the graph of \( y = x^2 \) up by 4 units.)

2. **Horizontal shift, 4 units to the right.**
Equation: **B. \( y = (x - 4)^2 \)**
(This shifts the graph of \( y = x^2 \) to the right by 4 units.)

3. **Horizontal shift, 4 units to the left.**
Equation: **A. \( y = (x + 4)^2 \)**
(This shifts the graph of \( y = x^2 \) to the left by 4 units.)

4. **Vertical shift, 4 units down.**
Equation: **C. \( y = x^2 - 4 \)**
(This shifts the graph of \( y = x^2 \) down by 4 units.)

So the matches are:
1 - D, 2 - B, 3 - A, 4 - C.