Question

Convert the equation from vertex form to standard form y = -4(x + 5)? - 3. (1 point)
• y = 16x2 + 160x + 412
0 y = -4x2 - 25x - 3
• y = 16x2 + 160x + 397
0 y = - 4x2 - 40x - 103

Answer 1

To convert the equation from vertex form to standard form, we start with the given vertex form equation:

\[ y = -4(x + 5)^2 - 3 \]

First, we will expand the equation:

1. Expand the square:
\[
(x + 5)^2 = x^2 + 10x + 25
\]

2. Substitute this back into the equation:
\[
y = -4(x^2 + 10x + 25) - 3
\]

3. Distribute the \(-4\):
\[
y = -4x^2 - 40x - 100 - 3
\]

4. Combine the constant terms:
\[
y = -4x^2 - 40x - 103
\]

Thus, the equation in standard form is:

\[
y = -4x^2 - 40x - 103
\]

So the correct answer is:

**y = -4x^2 - 40x - 103**.