Question

which of the following accurately depicts the transformation of y=x^2 to the function shown below? y=5(x-2)^2 + 1

Answer 1

The transformation of y=x^2 to the function y=5(x-2)^2 + 1 involves a horizontal shift to the right by 2 units, a vertical stretch by a factor of 5, and a vertical shift upward by 1 unit.

Step-by-step explanation:

The transformation of y = x^2 to the function y = 5(x-2)^2 + 1 can be described as a vertical and horizontal shift, and a vertical stretch. Here are the steps:

1. The term (x-2) in the function y = 5(x-2)^2 + 1 represents a horizontal shift to the right by 2 units. This means that each point on the graph is shifted 2 units to the right.
2. The term (x-2)^2 represents a vertical stretch of the original parabola y = x^2. The points on the graph are stretched vertically by a factor of 5 compared to the original parabola.
3. The term +1 represents a vertical shift upward by 1 unit. This means that each point on the graph is shifted upward by 1 unit.

Combining these transformations, the graph of y = x^2 is shifted 2 units to the right, stretched vertically by a factor of 5, and shifted upward by 1 unit to obtain the graph of y = 5(x-2)^2 + 1.