Question

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

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

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=−4x2−40x−103

Answer 1

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

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

First, we need to expand the squared term \((x + 5)^2\):

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

Now substituting this back into the equation:

\[
y = -4(x^2 + 10x + 25) - 3
\]

Next, we distribute \(-4\):

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

Now combine the constant terms:

\[
-100 - 3 = -103
\]

So, we have:

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

Thus, the standard form of the equation is:

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

So the correct response is:

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