Questions: The graph above is a transformation of the function f(x)=x^2 Write an equation for the function graphed above. g(x)=

The graph above is a transformation of the function f(x)=x^2 Write an equation for the function graphed above. g(x)=
Transcript text: The graph above is a transformation of the function $f(x)=x^{2}$ Write an equation for the function graphed above. \[ g(x)= \]
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Solution

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Solution Steps

Step 1: Identify the Parent Function

The parent function given is \( f(x) = x^2 \).

Step 2: Analyze the Transformation

Observe the graph to determine the transformations applied to the parent function. The graph appears to be a downward parabola, indicating a vertical reflection. Additionally, the vertex of the parabola is at (0, 3), indicating a vertical shift.

Step 3: Write the Transformed Function

The vertical reflection means the function is multiplied by -1, and the vertical shift up by 3 units means adding 3 to the function. Therefore, the transformed function is: \[ g(x) = -x^2 + 3 \]

Final Answer

\[ g(x) = -x^2 + 3 \]

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