Question

Question
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 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.
The parent function was translated 6 units to the left.
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Answer 1

To determine the translation of the parent function \( y = x^2 \), we need to analyze its vertex compared to the original form of the parabola.

The parent function \( y = x^2 \) has its vertex at the origin (0,0). If it has been translated horizontally, we can express this in the form \( y = (x - h)^2 \), where \( h \) indicates the horizontal translation.

To find how many units the function has been translated, we need to look for the x-coordinate of the vertex of the new parabola shown in the image.

If the vertex of the new parabola (the solid line) is at \( (h, k) \), then the translation can be determined by the value of \( h \):

1. If \( h < 0 \), the parabola was translated to the **left**.
2. If \( h > 0 \), the parabola was translated to the **right**.

From the given responses, if the vertex of the translated parabola is at \( (-5, k) \), then:

- The parent function was translated \( 5 \) units to the left.

If it is at \( (6, k) \), then:

- The parent function was translated \( 6 \) units to the right.

For every value you see in the choices, you evaluate where the vertex of the translated parabola would be in context of the origin to conclude the translation direction and distance.

Since I do not have access to the image, if you find that the new vertex is at \( -5 \) (less than 0), the answer to choose from your options would be:

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

If you find that it is at \( +6 \), then choose:

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

Make sure to confirm the vertex position from the graph in the image to select the correct answer!