Question

The vertex form of a function is g(x)=(x−3)²+9. How does the graph of g(x) compare to the graph of the function 2f(x)=x²?

a) g(x) is shifted 3 units left and 9 units up.
b) g(x) is shifted 3 units right and 9 units up.
c) g(x) is shifted 9 units left and 3 units down.
d) g(x) is shifted 9 units right and 3 units down.

Answer 1

The graph of g(x) is shifted 3 units to the right and 9 units up from the graph of f(x).

Step-by-step explanation:

The vertex form of a quadratic function is given by the equation g(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. In the equation g(x) = (x - 3)^2 + 9, we can see that the vertex is at (3, 9) and that the value of a is 1. Comparing this to the function 2f(x) = x^2, we can see that the graph of g(x) is shifted 3 units to the right and 9 units up from the graph of f(x).