Question

Match the equation on the left to its equivalent on the right.
y = x2+4x−2 =(____)
y=(x+4)2−12 =(____)
y=(x+15)(x+1) =(___)

Answer 1

To match the equations on the left to their equivalent forms on the right, we need to identify the forms through simplification or factoring.

1. **For the first equation**:
\( y = x^2 + 4x - 2 \)

We can complete the square:
\[
y = (x^2 + 4x + 4) - 4 - 2
\]
\[
y = (x + 2)^2 - 6
\]

This does not seem to match the given form directly.

Alternatively, we can simply recognize the equation form here.

2. **For the second equation**:
\( y = (x + 4)^2 - 12 \)

Expanding this:
\[
y = (x^2 + 8x + 16) - 12
\]
\[
y = x^2 + 8x + 4
\]

This does not seem to match the given form directly.

3. **For the third equation**:
\( y = (x + 15)(x + 1) \)

Expanding gives:
\[
y = x^2 + 16x + 15
\]

Now, let's set the matches:

- **First equation**: \(y = x^2 + 4x - 2\) must match with the forms we tried to complete. So:

\(y = x^2 + 4x - 2\) **matches with**

- **Second equation**:
\(y = (x + 4)^2 - 12\)

**matches with:**

- **Third equation**: \(y = (x + 15)(x + 1)\) **matches with**

Putting it together, the matches are (noting that there might've been a confusion in form):

1. \( y = x^2 + 4x - 2 = (x + 2)^2 - 6 \)
2. \( y = (x + 4)^2 - 12 = (x + 4)^2 - 12 \)
3. \( y = (x + 15)(x + 1) = x^2 + 16x + 15 \)

The equivalent forms are \[
y = x^2 + 4x - 2 \Rightarrow \text{(need to find corresponding) }
\]
\[
y = (x + 4)^2 - 12 \Rightarrow \text{(equivalent forms)}
\]
\[
y = (x + 15)(x + 1) \Rightarrow \text{(equivalent forms)}
\]

Colorful and explicit matching based on their expanded forms is encouraged.