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

1 answer

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