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 break down the given equations one by one and match them with their equivalents:

1. Starting with **y = x^2 - 1x - 20** (A):
To factor this, we find two numbers that multiply to -20 and add to -1:
- These numbers are -5 and 4, so we can factor it as **y = (x - 5)(x + 4)**, matching with C) y = (x + 4)(x - 5).

2. Next, **y = (x + 8)(x + 11)** (B):
We can expand this:
- y = x^2 + 11x + 8x + 88 = **y = x^2 + 19x + 88**, matching with D) y = x^2 + 19x + 88.

3. Now checking **y = x^2 - 6x + 16** (C):
We can complete the square or check for factors:
- Completing the square: y = (x - 3)^2 + 7. This matches with B) y = (x - 3)^2 + 7.

4. Finally, **y = (x + 4)^2 - 5** (D):
- Expanding this: y = (x^2 + 8x + 16 - 5) = x^2 + 8x + 11, but there are no further equivalents listed.

So here are the matches:

- **A)** y = x^2 - 1x - 20 → **C)** y = (x + 4)(x - 5)
- **B)** y = (x - 3)^2 + 7 → **C)** y = x^2 - 6x + 16
- **C)** y = (x + 4)(x - 5) → **A)** y = x^2 - 1x - 20
- **D)** y = x^2 + 19x + 88 → **B)** y = (x + 8)(x + 11)

Final matches:

1. A ↔ C
2. B ↔ C
3. C ↔ A
4. D ↔ B