Question

Match the equation on the left to its equivalent on the right.(3 points)

y=(x+6)^2−15

y = x^2 +x −12

y = x^2−8x+6

Answers

y = (x - 4)^2 - 10

y = x^2 + x - 12

y = x^2 - 8x + 6

Answer 1

Let's match the equations on the left to their equivalents on the right step by step.

1. **First Equation: \(y = (x + 6)^2 - 15\)**

Expanding \( (x + 6)^2 \):
\[
= x^2 + 12x + 36
\]
Now, subtracting 15:
\[
y = x^2 + 12x + 36 - 15
\]
\[
y = x^2 + 12x + 21
\]
This does not match any of the options provided yet.

2. **Second Equation: \(y = x^2 + x - 12\)**

This is already in standard form.

3. **Third Equation: \(y = x^2 - 8x + 6\)**

This is also in standard form.

Next, we need to match the equivalent answers:

1. **For the first equation \(y = (x + 6)^2 - 15\)**, we have a limited match with \( y = (x - 4)^2 - 10 \):
\[
(x - 4)^2 - 10 = x^2 - 8x + 16 - 10 = x^2 - 8x + 6
\]
So that option \( y = (x - 4)^2 - 10 \) corresponds to the equation \(y = x^2 - 8x + 6\).

For the other options:

2. **\(y = x^2 + x - 12\)** corresponds to \(y = x^2 + x - 12\).

So, the final matches are:
- \(y = (x + 6)^2 - 15\) matches neither provided.
- \(y = x^2 + x - 12\) matches \(y = x^2 + x - 12\).
- \(y = x^2 - 8x + 6\) matches \(y = (x - 4)^2 - 10\).

Thus, the answers can be summarized as:
- \(y = (x + 6)^2 - 15\) has no equivalent given,
- \(y = x^2 + x - 12\) matches \(y = x^2 + x - 12\),
- \(y = x^2 - 8x + 6\) can be transformed to \(y = (x - 4)^2 - 10\).

Since it seems your equation would want only direct matches and those are set.

Here’s the conclusion:

1. **\(y = (x + 6)^2 - 15\)** does not match the given answers.
2. **\(y = x^2 + x - 12\)** matches with \(y = x^2 + x - 12\).
3. **\(y = x^2 - 8x + 6\)** matches with \(y = (x - 4)^2 - 10\).

Please ensure to check the question specifics again in case of specific additional options matching.