A coordinate plane's x-axis ranges from negative 9 to 9 and its y-axis ranges from negative 11 to 11, both by 1-unit increments. A concave up parabola labeled f of x equals x squared is plotted passing through 7 marked points. A parabola that opens upward and seven labeled points on the parabola are plotted on a coordinate plane. The parabola has bidirectional arrows and is labeled f left parenthesis x right parenthesis equals x squared baseline minus 3.

Question

The image shows a parent function f(x)=x2
and a translated form f(x)=x2−3
. Which statement best describes this translation?

(1 point)
Responses

The parent function shifted horizontally to the right 3 units and did not change in any other way.
The parent function shifted horizontally to the right 3 units and did not change in any other way.

The function shifted vertically down 3 units and is wider than the original.
The function shifted vertically down 3 units and is wider than the original.

The function shifted horizontally to the right 3 units and is narrower than the original.
The function shifted horizontally to the right 3 units and is narrower than the original.

The parent function shifted vertically down 3 units and did not change in any other way.
The parent function shifted vertically down 3 units and did not change in any other way.

Answer 1

The correct statement that best describes the translation is:

The parent function shifted vertically down 3 units and did not change in any other way.

This is because the function \( f(x) = x^2 - 3 \) represents a vertical translation of the parent function \( f(x) = x^2 \) downwards by 3 units. There is no horizontal shift or change in the width of the parabola in this transformation.