Question

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

y=−4x2−40x−103
𝑦
=
−
4
𝑥
2
−
40
𝑥
−
103
y equals negative 4 x squared minus 40 x minus 103

y=16x2+160x+397
𝑦
=
16
𝑥
2
+

Answer 1

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

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

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

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

So the correct response is:
\[
y = -4x^2 - 40x - 103
\]