To determine the correct translation of the parent function \( y = x^2 \), we need to analyze the graph of the solid line (the parent function) and its position relative to the axes.
Typically, if the function is translated to the left, it will be in the form \( y = (x + k)^2 \), where \( k > 0 \) signifies a leftward shift. Conversely, if it is shifted to the right, the equation takes the form \( y = (x - k)^2 \), where \( k > 0 \) signifies a rightward shift.
Without visually inspecting the image, I would suggest that if you provide the coordinates of the vertex of both parabolas or their points of intersection with the y-axis, I might be able to help you more precisely in determining whether the translation was to the left or right, and by how many units.
However, from your responses:
- 5 units to the left
- 6 units to the right
- 5 units to the right
- 6 units to the left
It sounds like there are two distinct possible translations (5 or 6 units) and both directions (left or right). If you can identify the vertex of the parent function and compare it to the new position, you can determine how many units and in which direction it has been moved.
Please check the graph to see how far the vertex of the parabola shifted horizontally from \( x = 0 \). Based on those calculations, you would choose the appropriate option from the responses provided.