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

Solution

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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