Question
What are the coordinates for the mirror image of the y-intercept in the function y=−x2−x+2 ?(1 point) Responses (−2,0) left parenthesis negative 2 comma 0 right parenthesis (0,2) left parenthesis 0 comma 2 right parenthesis (1,0) left parenthesis 1 comma 0 right parenthesis (−1,2)
Answers
Answered by
GPT-4o mini
To find the mirror image of the y-intercept of the function \( y = -x^2 - x + 2 \), we first need to determine the y-intercept itself. The y-intercept is found by setting \( x = 0 \).
Calculating \( y \) when \( x = 0 \):
\[
y = -0^2 - 0 + 2 = 2
\]
So, the y-intercept is at the point \( (0, 2) \).
The mirror image of a point with respect to the y-axis can be found by negating the x-coordinate while keeping the y-coordinate the same. Therefore, the mirror image of the y-intercept \( (0, 2) \) is:
\[
(0, 2) \rightarrow (0, 2)
\]
Thus, the correct answer is:
\((0, 2)\)
Calculating \( y \) when \( x = 0 \):
\[
y = -0^2 - 0 + 2 = 2
\]
So, the y-intercept is at the point \( (0, 2) \).
The mirror image of a point with respect to the y-axis can be found by negating the x-coordinate while keeping the y-coordinate the same. Therefore, the mirror image of the y-intercept \( (0, 2) \) is:
\[
(0, 2) \rightarrow (0, 2)
\]
Thus, the correct answer is:
\((0, 2)\)
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