Question

Match the equation on the left to its equivalent on the right.
y = x2 − 8x + 12
y = x2 + 4x − 2
y = (x + 4)2 − 12
y = (x + 15) (x + 1)

A) y = x^2 + 8x + 4
B) y = x^2 + 16x + 15
C) y = (x + 2)^2 - 6
D) y = (x - 2) (x - 6)

Answer 1

To match the equations on the left to their equivalent forms on the right, we'll manipulate the left-hand side equations into different forms or expand the right-hand side equations to find matches.

1. **y = x² - 8x + 12**
- Factor: y = (x - 2)(x - 6), which matches D.

2. **y = x² + 4x - 2**
- Complete the square:
y = (x + 2)² - 6, which matches C.

3. **y = (x + 4)² - 12**
- Expand:
y = (x² + 8x + 16 - 12) = x² + 8x + 4, which matches A.

4. **y = (x + 15)(x + 1)**
- Expand:
y = x² + 16x + 15, which matches B.

So the matches are:
- y = x² - 8x + 12 → D) y = (x - 2)(x - 6)
- y = x² + 4x - 2 → C) y = (x + 2)² - 6
- y = (x + 4)² - 12 → A) y = x² + 8x + 4
- y = (x + 15)(x + 1) → B) y = x² + 16x + 15