To determine how many units the parent function \( y = x^2 \) (the solid line) was translated, you need to compare the vertex of the transformed parabola to the vertex of the parent parabola.
The parent function \( y = x^2 \) has its vertex at the origin (0, 0). When the function is translated horizontally, it takes the form \( y = (x - h)^2 \), where \( h \) indicates how many units it has been shifted to the right or left. A positive \( h \) means a shift to the right, while a negative \( h \) indicates a shift to the left.
If you can observe the vertex of the given solid line parabola, you can determine how far it has been shifted from the origin.
- If the vertex of the parabolas is located at (5, 0), then the transformation is \( y = (x - 5)^2 \) which means the parabola was translated 5 units to the right.
- If the vertex is at (6, 0), then it was translated 6 units to the right.
- If the vertex is at (-5, 0), then it was translated 5 units to the left.
- If the vertex is at (-6, 0), then it was translated 6 units to the left.
Without the visual reference, you could select the correct response based on the described change in vertex position compared to the origin. Please identify the vertex and decide accordingly. If, for instance, the vertex is at (5,0), then the correct response would be:
"The parent function was translated 5 units to the right."
If it's at (-5,0), then the response would be:
"The parent function was translated 5 units to the left."
Evaluate the vertex from the image, and that will lead you to the correct answer.
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