Let's match the equations on the left with their equivalent forms on the right:
-
y = x² − 6x + 16
- This can be rewritten as: \(y = (x - 3)² + 7\) by completing the square.
- Match: y=(x-3)²+7
-
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
-
y = x² − 1x − 20
- This can be factored as: \(y = (x + 4)(x - 5)\).
- Match: y=(x+4)(x-5)
-
y = (x + 8)(x + 11)
- Expanding this results in: \(y = x² + 19x + 88\).
- Match: y=x²+19x+88
So the final matches are:
- y = x² − 6x + 16 → y=(x-3)²+7
- y = (x + 4)² − 5 → y=x²+8x+11
- y = x² − 1x − 20 → y=(x+4)(x-5)
- y = (x + 8)(x + 11) → y=x²+19x+88