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Graph of the transform function is shown determine the parent function in the equation of the transformed function there's a point at negative 3, 2 negative 2, 0 negative 1, 2

My parent function is y = x + 2 squared
The parent function is y equals x squared y = X + 2 squared
The parent function is y equals x squared y = x - 2 squared
Parent function is y equals x - 2 squared y equals x squared squared

1 answer

To determine the parent function from the given points and the transformed function \( y = (x + 2)^2 \), we need to analyze the transformation that has taken place.

Based on your description, it seems the transformation involves a shift and possibly other interpretations of the function. Here's how we break it down:

  1. Identifying the Parent Function: You suggested the parent function could be \( y = x^2 \) based on your options. In the context of the transformations:

    • If we have the function \( y = (x + 2)^2 \), this means that the graph of \( y = x^2 \) is shifted to the left by 2 units.

  2. Examine the Points:

    • You provided points at (-3, 2), (-2, 0), and (-1, 2). Let's see if these fit the transformation.

    For the parent function \( y = x^2 \):

    • The first point (-3, 2): When \( x = -3 \), \( y = (-3 + 2)^2 = (-1)^2 = 1 \). This does not match the point.
    • The second point (-2, 0): When \( x = -2 \), \( y = (-2 + 2)^2 = (0)^2 = 0 \). This matches the point.
    • The third point (-1, 2): When \( x = -1 \), \( y = (-1 + 2)^2 = (1)^2 = 1 \). This does not match the point.

    It seems like there might be an error in either the points provided or in the interpretation.

  3. Choosing the Correct Parent Function: From your options:

    • The parent function \( y = x^2 \) is a reasonable starting point.
    • The function \( y = (x - 2)^2 \) indicates a rightward shift.
    • The function \( y = (x + 2)^2 \) indicates a leftward shift.

Given that the original question states the form \( y = (x + c)^2 \) where it shifts left or right, and given the matching point at (-2, 0), the overall trend suggests the transformation might correspond to a left shift (if the algebra confirms other points).

Conclusion:

The parent function is likely \( y = x^2 \) with the transformation represented as \( y = (x + 2)^2 \). The expression \( y = (x + 2)^2 \) indicates a leftward shift by 2 units, which matches the function's form with respect to the points discussed.

If any additional information or verification of points is available, it would help in refining this conclusion further.