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

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.

Answer 1

To determine how many units the parent function \( y = x^2 \) was translated, you can compare the vertex of the parent function (which is at the origin \( (0, 0) \)) to the vertex of the translated function.

Without the actual image, I can provide the general approach:

1. Identify the vertex of the parent function \( y = x^2 \), which is at \( (0, 0) \).
2. Locate the vertex of the translated function on the graph.
3. Determine the horizontal distance between the original vertex and the translated vertex. A negative distance indicates a leftward translation, while a positive distance indicates a rightward translation.

• If the vertex of the translated function is at \( (-5, \text{some } y \text{ value}) \), then the function was translated 5 units to the left.
• If the vertex is at \( (6, \text{some } y \text{ value}) \), then it was translated 6 units to the right.
• If the vertex is at \( (5, \text{some } y \text{ value}) \), then it was translated 5 units to the right.
• If the vertex is at \( (-6, \text{some } y \text{ value}) \), then it was translated 6 units to the left.

Choose the correct option based on the position of the translated vertex relative to the original vertex at (0, 0).