Question

Match the equation on the left to its equivalent on the right.
y = x^2 - 1x - 20
y = (x + 8) (x + 11)
y = x^2 - 6x +16
y = (x + 4)^2 - 5
A) y = x ^2 - 1x - 20
B) y = (x - 3)^2 + 7
C) y = (x + 4) (x - 5)
D) y = x^2 + 19x + 88

Answer 1

Let's match the equations on the left with their correct equivalents on the right.

1. **For the equation \( y = x^2 - 1x - 20 \)**:
- To factor \( x^2 - x - 20 \), we look for two numbers that multiply to \(-20\) and add to \(-1\). The correct factors are \((x - 5)(x + 4)\).
- This matches with option **C)** \( y = (x + 4)(x - 5) \).

2. **For the equation \( y = (x + 8)(x + 11) \)**:
- Expanding \( (x + 8)(x + 11) \) gives \( x^2 + 19x + 88 \).
- This matches with option **D)** \( y = x^2 + 19x + 88 \).

3. **For the equation \( y = x^2 - 6x + 16 \)**:
- We can complete the square or find the vertex form. The quadratic shifts to vertex form as \( (x - 3)^2 + 7 \).
- This matches with option **B)** \( y = (x - 3)^2 + 7 \).

4. **For the equation \( y = (x + 4)^2 - 5 \)**:
- This is already in vertex form, but it does not match with any of the equations given.

In summary, the complete matching is as follows:
- \( y = x^2 - 1x - 20 \) matches with **C)**.
- \( y = (x + 8)(x + 11) \) matches with **D)**.
- \( y = x^2 - 6x + 16 \) matches with **B)**.
- \( y = (x + 4)^2 - 5 \) does not have a matching option provided.

Thus:
1. **A** -> **C**
2. **B** -> \( y = (x - 3)^2 + 7 \)
3. **D** -> \( y = x^2 + 19x + 88 \)
4. **No option matches \( (x + 4)^2 - 5 \)**.