Question

The parent function y=x2 is shown in black. What is the equation of the transformation shown in the dashed orange graph?

a) y=(x−2)^2
b) y=(x+2)^2
c) y=x^2+2
d) y=x^2−2

Answer 1

The equation of the transformation shown in the dashed orange graph is y=(x-2)^2.

Step-by-step explanation:

The parent function y=x2 is a quadratic function that opens upward and has its vertex at the origin (0,0). The transformation shown in the dashed orange graph is a horizontal shift to the right by 2 units.

When the graph is shifted to the right by 2 units, the equation becomes y=(x-2)2. This is because the positive value inside the parentheses represents the amount of the horizontal shift.

Therefore, the correct equation of the transformation shown in the dashed orange graph is y=(x-2)2 (option a).