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=16x2+160x+412
y
=
16
x
2
+
160
x
+
412
y equals 16 x squared plus 160 x plus 412

y=−4x2−25x−3
y
=
−
4
x
2
−
25
x
−
3
y equals negative 4 x squared minus 25 x minus 3

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

Answer 1

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

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

First, we expand the square:

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

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

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

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

So the standard form of the equation is:

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

From your responses, the correct choice is:

**y = −4x² − 40x − 103**