To determine the parent function and the equation of the transformed function from the options provided, we need to analyze the transformations described in the equations involving the function \( y = x^2 \).
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Identify the parent function: The parent function for a quadratic equation is \( y = x^2 \).
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Analyze transformations:
- Transformation involving \( (x-2)^2 \) indicates a horizontal shift to the right by 2 units.
- Transformation involving \( (x+2)^2 \) indicates a horizontal shift to the left by 2 units.
Given the provided options:
- A suggests transforming \( (x-2)^2\) from \( y = x^2\).
- B suggests transforming \( (x+2)^2\) from \( y = x^2\).
- C suggests the inverse: transforming \( (x-2)^2\) which means the function starts as \( y = x^2\) before moving.
- D suggests \( (x+2)^2\) is transformed from \( y=x^2\).
To deduce correctly:
- If the transformed function is \( y = (x - 2)^2 \), the parent function is \( y = x^2 \).
- If the transformed function is \( y = (x + 2)^2 \), the parent function is also \( y = x^2 \).
The only correct match for identifying standard transformations practiced with parent functions while being tied to \( y = x^2 \) is option C.
Thus, the answer is:
C. The parent function is \( y = x^2 \). The equation of the transformed function is \( y = (x - 2)^2 \).
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