Question

Match the equation on the left to its equivalent on the right.
y = (x + 3)^2 − 8
y = (x + 9) (x + 1)
y = x^2 + 2x - 8
y = x^2 - 10x + 10

A) y = x^2 + 10x + 9
B) y = (x - 2) (x - 8)
C) y = (x + 1)^2 - 9
D) y = x^2 + 6x + 1

Answer 1

Let's match each equation on the left with its equivalent on the right.

1. **y = (x + 3)^2 − 8**
- Expanding this:
\[
= x^2 + 6x + 9 - 8 = x^2 + 6x + 1
\]
- This matches with **D) y = x^2 + 6x + 1**.

2. **y = (x + 9) (x + 1)**
- Expanding this:
\[
= x^2 + 10x + 9
\]
- This matches with **A) y = x^2 + 10x + 9**.

3. **y = x^2 + 2x - 8**
- To factor this:
\[
y = (x - 2)(x + 4) \text{ (not directly from the provided options)}
\]
- There isn't an option that directly corresponds, so we leave it unmatched for now.

4. **y = x^2 - 10x + 10**
- This can be rewritten as:
\[
= (x - 5)^2 - 15 \text{ (not directly from the provided options)}
\]
- It seems like it doesn't match any given options either.

After reassessing these calculations, the matches we have arrive as follows:

- **y = (x + 3)^2 − 8** matches with **D**.
- **y = (x + 9) (x + 1)** matches with **A**.

The equations **y = x^2 + 2x - 8** and **y = x^2 - 10x + 10** do not have a matching option based on typical forms.

In conclusion:
- **(1)** matches with **D**
- **(2)** matches with **A**
- **(3)** and **(4)** do not match any of the options.