Questions: Graph the following quadratic function: f(x)=-1/2(x-4)^2+3

Transcript text: Graph the following quadratic function: \[ f(x)=\frac{-1}{2}(x-4)^{2}+3 \]

Solution

Solution Steps

Step 1: Identify the Function

The given quadratic function is: \[ f(x) = \frac{-1}{2}(x-4)^{2} + 3 \]

Step 2: Determine the Vertex

The function is in vertex form $ f(x) = a(x-h)^2 + k $, where $ a = -\frac{1}{2} $, $ h = 4 $, and $ k = 3 $. Thus, the vertex of the parabola is at $ (4, 3) $.

Step 3: Determine the Direction of the Parabola

Since $ a = -\frac{1}{2} $ is negative, the parabola opens downwards.

Final Answer

The quadratic function $ f(x) = \frac{-1}{2}(x-4)^{2} + 3 $ is a downward-opening parabola with a vertex at $ (4, 3) $.

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 8, "ymin": 0, "ymax": 5}, "commands": ["y = (-1/2)*(x-4)**2 + 3"], "latex_expressions": ["$y = \\frac{-1}{2}(x-4)^{2} + 3$"]}

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