Question

The parent function is y=x². Given that the new function is y=−2(x−3)², which of the following transformations occurred?

A) Vertical compression by a factor of 2 and horizontal shift 3 units to the right.
B) Vertical stretch by a factor of 2 and horizontal shift 3 units to the left.
C) Vertical compression by a factor of 2 and horizontal shift 3 units to the left.
D) Vertical stretch by a factor of 2 and horizontal shift 3 units to the right.

Answer 1

The function y=−2(x−3)² represents a vertical compression by a factor of 2 and a horizontal shift 3 units to the right.

Step-by-step explanation:

The parent function y=x² is transformed into y=−2(x−3)². To determine the transformations that occurred, we can compare the new function to the parent function. The negative sign in front of the function reflects the graph vertically downward, resulting in a vertical reflection. The factor of -2 outside the function compresses the graph vertically by a factor of 2. Finally, the (x-3) term inside the function represents a horizontal shift 3 units to the right.

Therefore, the correct answer is:

A) Vertical compression by a factor of 2 and horizontal shift 3 units to the right.