Question

Match the equations to their equivalent in the options:
y = x^2 + 2x - 8
y = x^2 - 10x + 16
Options:
y = (x + 1)^2 - 9 (the only ^ was the 2, the -9 was not in the ^ as well)
y = (x - 2) (x - 8)

Answer 1

To match the equations to their equivalent forms, let's analyze both given equations and the options.

### Given equations:
1. **Equation 1:** \( y = x^2 + 2x - 8 \)
2. **Equation 2:** \( y = x^2 - 10x + 16 \)

### Options:
1. \( y = (x + 1)^2 - 9 \)
2. \( y = (x - 2)(x - 8) \)

### Let's convert both equations into different forms:

**For Equation 1: \( y = x^2 + 2x - 8 \)**
1. We can complete the square:
- \( y = (x^2 + 2x + 1) - 1 - 8 \)
- \( y = (x + 1)^2 - 9 \)

This matches with Option 1.

**For Equation 2: \( y = x^2 - 10x + 16 \)**
1. We can factor the quadratic:
- \( y = (x - 2)(x - 8) \)

This matches with Option 2.

### Summary of Matching:
- **Equation 1**: \( y = (x + 1)^2 - 9 \) (Option 1)
- **Equation 2**: \( y = (x - 2)(x - 8) \) (Option 2)

So:
- **Equation 1 → Option 1**
- **Equation 2 → Option 2**