Match the equations to their equivalent in the options:

Question

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