Question

Convert the equation from vertex form to standard form y=−4(x+5)2−3

Responses

y=−4x^2−25x−3

y=16x^2+160x+412

y=−4x^2−40x−103

y=16x^2+160x+397

Answer 1

To convert the equation \( y = -4(x + 5)^2 - 3 \) from vertex form to standard form, we will first expand the equation.

1. Start with the vertex form:
\[
y = -4(x + 5)^2 - 3
\]

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

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

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

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

Thus, the standard form of the equation is:
\[
\boxed{y = -4x^2 - 40x - 103}
\]

This matches one of the given responses.