Match the equation on the left to its equivalent on the right.

Question

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

A) y = x^2 + 10x + 9
B) y = (x - 2) (x - 8)
C) y = (x + 1)^2 -9
D) y = x^2 + 6x + 1

Answer 1

Let's match the equations on the left to their equivalent ones on the right.

1. For \( y = (x + 3)^2 - 8 \)

   We simplify the expression:

   \[ y = (x + 3)^2 - 8 = (x^2 + 6x + 9) - 8 = x^2 + 6x + 1 \]

   Match: \(D) y = x^2 + 6x + 1\)

2. For \( y = (x + 9)(x + 1) \)

   We expand the expression:

   \[ y = (x + 9)(x + 1) = x^2 + 10x + 9 \]

   Match: \(A) y = x^2 + 10x + 9\)

3. For \( y = x^2 + 2x - 8 \)

   This equation does not have an explicit initialization but can be left as is for matching as none of the other options directly correspond to it.

4. For \( y = x^2 - 10x + 10 \)

   Factorizing or completing the square is not necessary here for matching, as we have no corresponding option.

Now, let's summarize the matches:

• \( y = (x + 3)^2 - 8 \) matches with \( D) y = x^2 + 6x + 1 \)
• \( y = (x + 9)(x + 1) \) matches with \( A) y = x^2 + 10x + 9 \)

Remaining equations are unmapped so we state:

• \( y = x^2 + 2x - 8 \)
• \( y = x^2 - 10x + 10 \)

They remain unmatched to the given options. The available matches effectively lead to:

1. \(D) y = x^2 + 6x + 1 \) - from \( y = (x + 3)^2 - 8 \)
2. \(A) y = x^2 + 10x + 9 \) - from \( y = (x + 9)(x + 1) \)

Thus, the matched equations are \( D \) and \( A \) correctly aligned, with others remaining unpaired.