To determine the parent function and the equation of the transformed function from the given parabola, we need to analyze the transformations applied to the parent function \( y = x^2 \).
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The parent function is the basic function that describes the shape of the graph. The parent function for parabolas is \( y = x^2 \).
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The transformed function may be derived from the parent function by applying transformations such as translations (shifts), reflections, or stretches/compressions.
If the graph has been shifted horizontally or applied with other transformations like stretching, we can determine the transformed function based on the movements observed:
- If the graph appears to be moved to the left by 2 units, the equation would be \( y = (x + 2)^2 \).
- If the graph appears to be moved to the right by 2 units, the equation would be \( y = (x - 2)^2 \).
Since I don't have the visual of the graph, I can't determine with certainty whether the parabola shifts left or right solely from the given options. However, in your options, the transformation typically could look like one of these pairs:
- Option 1: Parent function \( y = (x + 2)^2 \) and transformed function \( y = x^2 \)
- Option 2: Parent function \( y = x^2 \) and transformed function \( y = (x - 2)^2 \)
- Option 3: Parent function \( y = x^2 \) and transformed function \( y = (x + 2)^2 \)
- Option 4: Parent function \( y = (x - 2)^2 \) and transformed function \( y = x^2 \)
Based on approximation and direction of shifts, if the graph indicates a leftward shift of 2 units:
Correct Answer: The parent function is \( y = x^2 \) and the equation of the transformed function is \( y = (x + 2)^2 \).
So, that would be Option 3: The parent function is \( y = x^2 \). The equation of the transformed function is \( y = (x + 2)^2 \).
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