Question

Question
Convert the equation from vertex form to standard form y=−4(x+5)2−3 .(1 point)
Responses

y=−4x2−25x−3
y equals negative 4 x squared minus 25 x minus 3

y=16x2+160x+397
y equals 16 x squared plus 160 x plus 397

y=16x2+160x+412
y equals 16 x squared plus 160 x plus 412

y=−4x2−40x−103
y equals negative 4 x squared minus 40 x minus 103
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Answer 1

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

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

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

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

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

Thus, the equation in standard form is:

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

The correct response is:
**y = -4x^2 - 40x - 103** (y equals negative 4 x squared minus 40 x minus 103).