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 6 units to the left.
The parent function was translated 6 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 5 units to the left.

Answer 1

To determine how many units the parent function \( y = x^2 \) has been translated, we need to find the vertex of the solid line parabola shown in the image compared to the standard vertex of the parent function, which is at the origin (0, 0).

If the vertex of the translated parabola is at \((h, k)\), the translation can be expressed as \( y = (x - h)^2 + k \). A leftward translation corresponds to a positive \( h \) (i.e., the function shifts left as \( h \) decreases) and a rightward translation corresponds to a negative \( h \).

Assuming the vertex of the translated parabola is at \((-6, 0)\) (you would replace this with the actual vertex position if you can see the image), the calculation would be:

• The parent function is at \( (0, 0) \).
• The new vertex is at \( (-6, 0) \).

To find the horizontal translation:

• The difference in the x-coordinates: \( -6 - 0 = -6 \) units.

This indicates the vertex is shifted 6 units to the left.

Thus, the correct answer would be:

The parent function was translated 6 units to the left.