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Match the equations to their equivalent in the options:

y = x^2 + 2x - 8
y = x^2 - 10x + 16
y = (x + 9) (x + 1)
y = (x + 3)^2 - 8

1 answer

Let's analyze each equation to find their equivalent forms:

  1. y = x^2 + 2x - 8:

    • This is already in standard form.

  2. y = x^2 - 10x + 16:

    • This is also in standard form.

  3. y = (x + 9)(x + 1):

    • To expand this, we use the distributive property: \[ y = x^2 + 10x + 9 \]

  4. y = (x + 3)^2 - 8:

    • First, expand \((x + 3)^2\): \[ (x + 3)^2 = x^2 + 6x + 9 \]
    • Then subtract 8: \[ y = x^2 + 6x + 9 - 8 = x^2 + 6x + 1 \]

Now, we summarize the equations we have:

  • \(y = x^2 + 2x - 8\)
  • \(y = x^2 - 10x + 16\)
  • \(y = x^2 + 10x + 9\)
  • \(y = x^2 + 6x + 1\)

Now we check for equivalent forms:

  • The first equation \(y = x^2 + 2x - 8\) has no matches among the expanded forms.
  • The second equation \(y = x^2 - 10x + 16\) has no matches either.
  • The third equation \(y = x^2 + 10x + 9\) corresponds to \(y = (x + 9)(x + 1)\).
  • The fourth equation \(y = x^2 + 6x + 1\) corresponds to \(y = (x + 3)^2 - 8\).

In conclusion, the matching pairs are:

  • \(y = (x + 9)(x + 1)\) is equivalent to \(y = x^2 + 10x + 9\).
  • \(y = (x + 3)^2 - 8\) is equivalent to \(y = x^2 + 6x + 1\).
  • The first two equations do not have equivalents among the options provided.