Use the image to answer the question.

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

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

The parent function was translated 6 units to the right.

Answer 1

To determine the translation of the parent function \( y = x^2 \), we would typically look at the vertex of the parabolas. The vertex of the parent function \( y = x^2 \) is at (0,0).

If the solid line representing the parent function \( y = x^2 \) has been translated horizontally to a new vertex, we can find its new position.

Assuming we see the new vertex of the solid line, we look for a number that indicates how far it has moved from the original position at (0,0).

• If the new vertex of the solid line is at (5,0), the function has translated 5 units to the right.
• If it has moved to (-5,0), it translates 5 units to the left.
• For (-6,0), it translates 6 units to the left.
• For (6,0), it translates 6 units to the right.

Without the specific image to refer to, I can't provide an exact answer, but generally, the translation will be determined by the x-coordinate of the new vertex relative to the original.

Check the x-coordinate of the vertex of the solid parabola in the image, and use that coordinate to determine the correct response from the options provided.