Question

standard form of y=4(x+2)^2-8

Answer 1

To convert the equation \( y = 4(x + 2)^2 - 8 \) into standard form, we can expand the right-hand side.

1. Start with the equation:
\[
y = 4(x + 2)^2 - 8
\]

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

3. Substitute this back into the equation:
\[
y = 4(x^2 + 4x + 4) - 8
\]

4. Distribute the 4:
\[
y = 4x^2 + 16x + 16 - 8
\]

5. Simplify the equation:
\[
y = 4x^2 + 16x + 8
\]

So, the standard form of the equation is:
\[
y = 4x^2 + 16x + 8
\]