Question

How does the graph of f(x) = (x - 8)^2 + 4 compare to the parent function g(x) = x^2?

A. The graph of f(x) is a horizontal shift to the right by 8 units and a vertical shift up by 4 units compared to g(x).
B. The graph of f(x) is a vertical stretch by a factor of 4 and a horizontal shift to the right by 8 units compared to g(x).
C. The graph of f(x) is a horizontal stretch by a factor of 8 and a vertical shift up by 4 units compared to g(x).
D. The graph of f(x) is a vertical shift down by 8 units and a horizontal shift to the left by 4 units compared to g(x).

Answer 1

The graph of f(x) shifts to the right by 8 units and upward by 4 units from the parent function g(x), with no changes in shape.

Step-by-step explanation:

The comparison between the graph of f(x) = (x - 8)^2 + 4 and the parent function g(x) = x^2 involves changes in position and shape. In this case, the graph of f(x) does not undergo any stretching or compressing, meaning the shape of the parabola remains the same. However, it does experience transformations in terms of shifts: a horizontal shift to the right and a vertical shift upwards. Specifically, the term (x - 8) indicates a horizontal shift to the right by 8 units, and the +4 at the end of the function denotes a vertical shift up by 4 units.

This information leads to the conclusion that the correct answer is: A. The graph of f(x) is a horizontal shift to the right by 8 units and a vertical shift up by 4 units compared to g(x).