Let's break down the given equations one by one and match them with their equivalents:
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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).
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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.
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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.
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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:
- A ↔ C
- B ↔ C
- C ↔ A
- D ↔ B