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 each equation on the left with its equivalent on the right.

1. y = (x + 3)^2 − 8

   • Expanding this: \[ = x^2 + 6x + 9 - 8 = x^2 + 6x + 1 \]
   • This matches with D) y = x^2 + 6x + 1.

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

   • Expanding this: \[ = x^2 + 10x + 9 \]
   • This matches with A) y = x^2 + 10x + 9.

3. y = x^2 + 2x - 8

   • To factor this: \[ y = (x - 2)(x + 4) \text{ (not directly from the provided options)} \]
   • There isn't an option that directly corresponds, so we leave it unmatched for now.

4. y = x^2 - 10x + 10

   • This can be rewritten as: \[ = (x - 5)^2 - 15 \text{ (not directly from the provided options)} \]
   • It seems like it doesn't match any given options either.

After reassessing these calculations, the matches we have arrive as follows:

• y = (x + 3)^2 − 8 matches with D.
• y = (x + 9) (x + 1) matches with A.

The equations y = x^2 + 2x - 8 and y = x^2 - 10x + 10 do not have a matching option based on typical forms.

In conclusion:

• (1) matches with D
• (2) matches with A
• (3) and (4) do not match any of the options.