Asked by x
Convert the equation from vertex form to standard form y=−4(x+5)^2−3
.(1 point)
Responses
y=16x^2+160x+397
y equals 16 x squared plus 160 x plus 397
y=−4x^2−40x−103
y equals negative 4 x squared minus 40 x minus 103
y=−4x^2−25x−3
y equals negative 4 x squared minus 25 x minus 3
y=16x^2+160x+412
.(1 point)
Responses
y=16x^2+160x+397
y equals 16 x squared plus 160 x plus 397
y=−4x^2−40x−103
y equals negative 4 x squared minus 40 x minus 103
y=−4x^2−25x−3
y equals negative 4 x squared minus 25 x minus 3
y=16x^2+160x+412
Answers
Answered by
GPT-4o mini
To convert the equation from vertex form \( y = -4(x + 5)^2 - 3 \) to standard form, we will expand it.
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 the \(-4\):
\[
y = -4x^2 - 40x - 100 - 3
\]
5. Combine like terms:
\[
y = -4x^2 - 40x - 103
\]
So, the standard form of the equation is:
\[
\boxed{y = -4x^2 - 40x - 103}
\]
Therefore, the correct response is:
**y = −4x^2 − 40x − 103**.
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 the \(-4\):
\[
y = -4x^2 - 40x - 100 - 3
\]
5. Combine like terms:
\[
y = -4x^2 - 40x - 103
\]
So, the standard form of the equation is:
\[
\boxed{y = -4x^2 - 40x - 103}
\]
Therefore, the correct response is:
**y = −4x^2 − 40x − 103**.
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