Questions: Graph the function. f(x)=-(x-3)^2 Choose the correct graph on the right. A. C. B. D.

Transcript text: Points: 0 of 1 Graph the function. \[ f(x)=-(x-3)^{2} \] Choose the correct graph on the right. A. C. $B$. D.

Solution

Solution Steps

Step 1: Identify the function

The given function is $ f(x) = -(x - 3)^2 $.

Step 2: Determine the vertex of the parabola

The function $ f(x) = -(x - 3)^2 $ is a parabola in vertex form $ f(x) = a(x - h)^2 + k $, where the vertex is at $ (h, k) $. Here, $ h = 3 $ and $ k = 0 $, so the vertex is at $ (3, 0) $.

Step 3: Determine the direction of the parabola

Since the coefficient of the squared term is negative ($ -1 $), the parabola opens downwards.

Final Answer

The correct graph is the one that has a vertex at $ (3, 0) $ and opens downwards. This corresponds to option A.

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