To determine the parent function and the equation of the transformed function from a parabola on a coordinate plane, we need to identify any shifts, stretches, or reflections that have occurred compared to the standard quadratic function.
The standard (parent) function for a parabola is \( y = x^2 \).
From the options provided, let's analyze them:
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If the transformed function has a form of \( y = (x+2)^2 \), this indicates a horizontal shift to the left by 2 units. This means the parent function is still \( y = x^2 \).
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If the transformed function had a form of \( y = (x-2)^2 \), this indicates a horizontal shift to the right by 2 units, with the parent function still being \( y = x^2 \).
Based on the responses provided, if the transformed function is given as \( y = (x + 2)^2 \), we would identify the parent function as \( y = x^2 \).
So, assuming that we are looking for the standard transformations of the parent function \( y = x^2 \) that results in the given transformed functions, the correct response seems to be:
The parent function is \( y = x^2 \). The equation of the transformed function is \( y = (x + 2)^2 \).
If the graph shifts to the left by 2 units, then that fits the description.
Thus, the option that best represents this is: The parent function is \( y = x^2 \). The equation of the transformed function is \( y = (x+2)^2 \).
1 answer