Use the image to answer the question.

Two parabolas drawn on coordinate plane. X-axis range from negative 9 to 4 and y-axis range from negative 1 to 9 in unit increment.

Which of the following correctly determines how many k units the parent function y=x2
(shown as a solid line) was translated?

(1 point)
Responses

The parent function was translated 6 units to the left.
The parent function was translated 6 units to the left.

The parent function was translated 6 units to the right.
The parent function was translated 6 units to the right.

The parent function was translated 5 units to the left.
The parent function was translated 5 units to the left.

The parent function was translated 5 units to the right

1 answer

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.