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

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

The parent function was translated 6 units to the left.

Answer 1

To determine how many units the parent function \( y = x^2 \) was translated, we need to look at the vertex of the transformed parabola in relation to the vertex of the parent function.

The parent function \( y = x^2 \) has its vertex at the origin (0,0). When a parabola is translated horizontally, its vertex moves left or right along the x-axis.

Since I cannot see the image, I will explain how to find the translation.

1. Identify the vertex of the solid line parabola \( y = x^2 \). If it remains at the origin (0,0), then it has not been translated.

2. If the vertex of the solid line parabola is, for example, at (5,0), then it has been translated 5 units to the right because you move from 0 to 5 on the x-axis.

3. If the vertex of the transformed parabola is at (-6,0), then it has been translated 6 units to the left.

Compare the x-coordinates based on the potential responses to determine the correct translation direction and distance.

Using this method with the image you have, identify the vertex and compare it to the original vertex (0,0) to find the appropriate option.