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Which function has a vertex at the origin? $f(x)=(x+4)^{2}$ $f(x)=x(x-4)$ $f(x)=(x-4)(x+4)$ $f(x)=-x^{2}$

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Frank

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Solution By Steps

Step 1: Identify the vertex of the function

The vertex of a quadratic function f(x) = a(x - h)^2 + k is located at the point (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.

Step 2: Determine the function with a vertex at the origin

The function with a vertex at the origin (0, 0) is f(x) = x^2, which corresponds to the option f(x) = -x^2.

Final Answer

The function that has a vertex at the origin is f(x) = -x^2.

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