Question

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

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

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

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

y=−4x2−40x−103

Answer 1

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

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

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

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

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

Therefore, the correct response is:
**y = −4x² − 40x − 103**.