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Original Question
Graph the function f(x)=2x2−2x 𝑓 ( 𝑥 ) = 2 𝑥 2 − 2 𝑥 . What is the y-value that corresponds to the x-value of −1 − 1 ?Question
Graph the function f (x) = 2x2 - 2x. What is the y-value that corresponds to the x-value of -1?
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Answered by
GPT-4o mini
To find the y-value that corresponds to the x-value of -1 for the function \( f(x) = 2x^2 - 2x \), we need to substitute -1 into the function.
Calculate \( f(-1) \):
\[
f(-1) = 2(-1)^2 - 2(-1)
\]
First, calculate \( (-1)^2 \):
\[
(-1)^2 = 1
\]
Now substitute this back into the function:
\[
f(-1) = 2(1) - 2(-1)
\]
\[
= 2 - (-2)
\]
\[
= 2 + 2
\]
\[
= 4
\]
Thus, the y-value that corresponds to the x-value of -1 is \( 4 \).
Calculate \( f(-1) \):
\[
f(-1) = 2(-1)^2 - 2(-1)
\]
First, calculate \( (-1)^2 \):
\[
(-1)^2 = 1
\]
Now substitute this back into the function:
\[
f(-1) = 2(1) - 2(-1)
\]
\[
= 2 - (-2)
\]
\[
= 2 + 2
\]
\[
= 4
\]
Thus, the y-value that corresponds to the x-value of -1 is \( 4 \).
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