To determine the translation of the parent function \( y = x^2 \) (which is centered at the origin), we need to identify the vertex of the given parabolas in the image.
The standard form for a vertically translated parabola is \( y = (x - h)^2 + k \). The value \( h \) indicates the horizontal translation and can be interpreted as follows:
- If \( h > 0 \), the graph is translated \( h \) units to the right.
- If \( h < 0 \), the graph is translated \( |h| \) units to the left.
If we assume that the vertex of the parent function \( y = x^2 \) is at (0, 0), and you provide the coordinates of the vertex of the translated parabolas, you can calculate the translation.
Since I do not have access to the image you mentioned, let's say, for example, the vertex of the solid line representing the parent function \( y = x^2 \) remains at (0, 0) and the vertex of the transformed function is located at (-6, 0). In that case, it would suggest that the parent function was translated 6 units to the left because:
- Translation from (0, 0) to (-6, 0) indicates a leftward shift.
If the vertex of the solid line was instead at (5, 0), then it would indicate translation 5 units to the right.
Please check the image's vertex coordinates to determine the appropriate translation. Based on the options given, if the vertex has shifted to the left by 6 units, then the correct response would be:
The parent function was translated 6 units to the left.
If it has shifted 5 units to the left or right, choose accordingly.