Question

Match the equation on the left to its equivalent on the right. (4 points)

y = x2−6x+16 =
y=(x+4)2−5 =
y = x2 − 1x −20 =
y=(x+8)(x+11) =
answers:
y=(x-3)^2+7
y=x^2+8x+11
y=(x+4)(x-5)
y=x^2+19x+88

Answer 1

Let's match the equations on the left with their equivalent forms on the right:

1. **y = x² − 6x + 16**
- This can be rewritten as: \(y = (x - 3)² + 7\) by completing the square.
- **Match: y=(x-3)²+7**

2. **y = (x + 4)² − 5**
- Expanding this yields: \(y = x² + 8x + 16 - 5\) which simplifies to \(y = x² + 8x + 11\).
- **Match: y=x²+8x+11**

3. **y = x² − 1x − 20**
- This can be factored as: \(y = (x + 4)(x - 5)\).
- **Match: y=(x+4)(x-5)**

4. **y = (x + 8)(x + 11)**
- Expanding this results in: \(y = x² + 19x + 88\).
- **Match: y=x²+19x+88**

So the final matches are:

1. y = x² − 6x + 16 → y=(x-3)²+7
2. y = (x + 4)² − 5 → y=x²+8x+11
3. y = x² − 1x − 20 → y=(x+4)(x-5)
4. y = (x + 8)(x + 11) → y=x²+19x+88