Questions: You can retry this question below The graph above is a transformation of the function (x^2) Write an equation for the function graphed above (g(x)=) Question Help: Message instructor Check Answer

You can retry this question below The graph above is a transformation of the function (x^2) Write an equation for the function graphed above (g(x)=) Question Help: Message instructor Check Answer
Transcript text: You can retry this question below The graph above is a transformation of the function $x^{2}$ Write an equation for the function graphed above \[ g(x)= \] $\square$ Question Help: Message instructor Check Answer
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Solution

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Solution Steps

Step 1: Identify the Vertex of the Parabola

The vertex of the parabola is at the point \((2, -4)\).

Step 2: Determine the Transformation

The given function \(x^2\) has been shifted right by 2 units and down by 4 units.

Step 3: Write the Equation

The transformation of \(x^2\) to the vertex form \(a(x-h)^2 + k\) where \(h = 2\) and \(k = -4\) results in the equation: \[ g(x) = (x - 2)^2 - 4 \]

Final Answer

\[ g(x) = (x - 2)^2 - 4 \]

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