Question

match each questions that are equivalent

y = x^2 − 8x + 12

y = x^2+4x−2

y=(x+4)^2−12

y=(x+15)(x+1)

answers

y = x^2 + 8x + 4

y = x^2 + 16x + 15

y = (x + 2)^2 - 6

y = (x - 2) (x - 6)

Answer 1

To match the given equations with their equivalent ones, we need to rewrite each of the equations provided and compare.

1. **For** \( y = x^2 - 8x + 12 \)

This can be factored:
\[
y = (x - 2)(x - 6)
\]

So, this matches with:
- **\( y = (x - 2)(x - 6) \)**

2. **For** \( y = x^2 + 4x - 2 \)

This can be rearranged into vertex form:
\[
y = (x + 2)^2 - 6
\]

So, this matches with:
- **\( y = (x + 2)^2 - 6 \)**

3. **For** \( y = x^2 + 4x - 2 \)**

This can be further analyzed but doesn't match directly, let's examine combinatory forms after isolation.

4. **For** \( y = (x + 4)^2 - 12 \)

This expands to:
\[
y = x^2 + 8x + 4
\]

So, this matches with:
- **\( y = x^2 + 8x + 4 \)**

5. **For** \( y = (x + 15)(x + 1) \)

This expands to:
\[
y = x^2 + 16x + 15
\]

So, this matches with:
- **\( y = x^2 + 16x + 15 \)**

### Summary of Matches:
- \( y = x^2 - 8x + 12 \) matches with \( y = (x - 2)(x - 6) \)
- \( y = x^2 + 4x - 2 \) matches with \( y = (x + 2)^2 - 6 \)
- \( y = (x + 4)^2 - 12 \) matches with \( y = x^2 + 8x + 4 \)
- \( y = (x + 15)(x + 1) \) matches with \( y = x^2 + 16x + 15 \)

These matchings denote equivalent expressions through direct algebraic manipulations like factoring and expanding.