Question

Match the equation on the left to its equivalent below
Equations: y = x^2 - 6x + 16, y = (x+8) (x+11), y = x^2 - 1x - 20, y = (x + 4)^2 - 5.
Equivalents: y = (x+4)(x-5), y = (x-3)^2 + 7, y = x^2 + 19x + 88, y = x^2 + 8x + 11

Answer 1

To match each equation to its equivalent, we will simplify and factor each one as needed.

1. **For** \( y = x^2 - 6x + 16 \):
We can complete the square or look for factorizations, but it seems simpler to check and arrive at its equivalent:
\[
y = (x - 3)^2 + 7
\]
This shows that the vertex form of the quadratic confirms it's equivalent.

2. **For** \( y = (x + 8)(x + 11) \):
Expanding this:
\[
y = x^2 + 19x + 88
\]
This matches with \( y = x^2 + 19x + 88 \).

3. **For** \( y = x^2 - 1x - 20 \):
To factor this, we look for two numbers that multiply to -20 and add to -1. We find:
\[
y = (x + 4)(x - 5)
\]

4. **For** \( y = (x + 4)^2 - 5 \):
Expanding gives:
\[
y = x^2 + 8x + 16 - 5 = x^2 + 8x + 11
\]

In summary, the matches are:
1. \( y = x^2 - 6x + 16 \) → \( y = (x - 3)^2 + 7 \)
2. \( y = (x + 8)(x + 11) \) → \( y = x^2 + 19x + 88 \)
3. \( y = x^2 - 1x - 20 \) → \( y = (x + 4)(x - 5) \)
4. \( y = (x + 4)^2 - 5 \) → \( y = x^2 + 8x + 11 \)