Question

Match the equations to their equivalent in the options:
y = x^2 + 2x - 8
y = x^2 - 10x + 16
y = (x + 9) (x + 1)
y = (x + 3)^2 - 8

Answer 1

Let's analyze each equation to find their equivalent forms:

1. **y = x^2 + 2x - 8**:
- This is already in standard form.

2. **y = x^2 - 10x + 16**:
- This is also in standard form.

3. **y = (x + 9)(x + 1)**:
- To expand this, we use the distributive property:
\[
y = x^2 + 10x + 9
\]

4. **y = (x + 3)^2 - 8**:
- First, expand \((x + 3)^2\):
\[
(x + 3)^2 = x^2 + 6x + 9
\]
- Then subtract 8:
\[
y = x^2 + 6x + 9 - 8 = x^2 + 6x + 1
\]

Now, we summarize the equations we have:
- \(y = x^2 + 2x - 8\)
- \(y = x^2 - 10x + 16\)
- \(y = x^2 + 10x + 9\)
- \(y = x^2 + 6x + 1\)

Now we check for equivalent forms:
- The first equation \(y = x^2 + 2x - 8\) has no matches among the expanded forms.
- The second equation \(y = x^2 - 10x + 16\) has no matches either.
- The third equation \(y = x^2 + 10x + 9\) corresponds to \(y = (x + 9)(x + 1)\).
- The fourth equation \(y = x^2 + 6x + 1\) corresponds to \(y = (x + 3)^2 - 8\).

In conclusion, the matching pairs are:
- \(y = (x + 9)(x + 1)\) is equivalent to \(y = x^2 + 10x + 9\).
- \(y = (x + 3)^2 - 8\) is equivalent to \(y = x^2 + 6x + 1\).
- The first two equations do not have equivalents among the options provided.