Question

Convert the quadratic y = (x + 4)2 − 5 from vertex form to standard form.
A) y = x^2 + 4x + 16
B) y = x^2 + 8x + 11
C) y = x^2 + 3
D) y = x^2 + 11

Answer 1

To convert the quadratic from vertex form \( y = (x + 4)^2 - 5 \) to standard form, we need to expand the expression.

1. Start with the vertex form:
\[
y = (x + 4)^2 - 5
\]

2. Expand \( (x + 4)^2 \):
\[
(x + 4)^2 = x^2 + 8x + 16
\]

3. Substitute this back into the equation:
\[
y = x^2 + 8x + 16 - 5
\]

4. Simplify:
\[
y = x^2 + 8x + 11
\]

Thus, the standard form of the quadratic is:
\[
y = x^2 + 8x + 11
\]

The correct answer is:
**B) \( y = x^2 + 8x + 11 \)**.