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Which of the following is the graph of
-x^(2)

Which of the following is the graph of $-x^{2}$

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Domain and range of quadratic functions: equations

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Q. Which of the following is the graph of

-x^{2}

Identify Graph Shape: Identify the general shape of the graph for the function $y = -x^2$ . Since the coefficient of $x^2$ is negative, the parabola opens downward.
Determine Vertex: Determine the vertex of the parabola. $\newline$ For the function $y = -x^2$ , the vertex is at the origin $(0, 0)$ because there is no $h$ or $k$ in the vertex form $y = a(x-h)^2 + k$ .
Check Symmetry: Check for symmetry. $\newline$ The graph of $y = -x^2$ is symmetric about the $y$ -axis because it is an even function.
Plot Points: Plot the vertex and a few points on either side of the vertex. The vertex is at $(0, 0)$ . Choosing $x = 1$ and $x = -1$ , we get $y = -1$ for both, so the points $(1, -1)$ and $(-1, -1)$ are on the graph. Choosing $x = 2$ and $x = -2$ , we get $y = -4$ for both, so the points $(2, -4)$ and $x = 1$ $0$ are on the graph.
Draw Parabola: Draw the parabola. Using the points and the knowledge that the parabola opens downward, draw a smooth curve through the points, making sure it is symmetric about the $y$ -axis and that it continues infinitely in both directions along the $x$ -axis.

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