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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

1 answer

Let's match the equations on the left with their correct equivalents on the right.

  1. For the equation \( y = x^2 - 1x - 20 \):

    • To factor \( x^2 - x - 20 \), we look for two numbers that multiply to \(-20\) and add to \(-1\). The correct factors are \((x - 5)(x + 4)\).
    • This matches with option C) \( y = (x + 4)(x - 5) \).

  2. For the equation \( y = (x + 8)(x + 11) \):

    • Expanding \( (x + 8)(x + 11) \) gives \( x^2 + 19x + 88 \).
    • This matches with option D) \( y = x^2 + 19x + 88 \).

  3. For the equation \( y = x^2 - 6x + 16 \):

    • We can complete the square or find the vertex form. The quadratic shifts to vertex form as \( (x - 3)^2 + 7 \).
    • This matches with option B) \( y = (x - 3)^2 + 7 \).

  4. For the equation \( y = (x + 4)^2 - 5 \):

    • This is already in vertex form, but it does not match with any of the equations given.

In summary, the complete matching is as follows:

  • \( y = x^2 - 1x - 20 \) matches with C).
  • \( y = (x + 8)(x + 11) \) matches with D).
  • \( y = x^2 - 6x + 16 \) matches with B).
  • \( y = (x + 4)^2 - 5 \) does not have a matching option provided.

Thus:

  1. A -> C
  2. B -> \( y = (x - 3)^2 + 7 \)
  3. D -> \( y = x^2 + 19x + 88 \)
  4. No option matches \( (x + 4)^2 - 5 \).