Question

Convert the equation from vertex form to standard form y=−4(x+5)2−3𝑦=−4(𝑥+5)2−3.(1 point)Responsesy=16x2+160x+412𝑦=16𝑥2+160𝑥+412y equals 16 x squared plus 160 x plus 412y=−4x2−25x−3𝑦=−4𝑥2−25𝑥−3y equals negative 4 x squared minus 25 x minus 3y=16x2+160x+397𝑦=16𝑥2+160𝑥+397y equals 16 x squared plus 160 x plus 397y=−4x2−40x−103

Answer 1

To convert the equation from vertex form \( y = -4(x + 5)^2 - 3 \) to standard form, we can follow these steps:

1. Start with the equation in 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 \(-4\):

\[
y = -4x^2 - 40x - 100 - 3
\]

5. Combine the constants:

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

Thus, the equation in standard form is:

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