Question

A quadratic function y=f(x) is plotted on a graph, and the vertex of the resulting parabola is (6, 3). What is the vertex of the function defined as g(x)=f(x+3)+2?

a. (3, 5).
b. (6, 3).
c. (9, 5).
d. (6, 5).

Answer 1

The vertex of the transformed function g(x) is (3, 5) after shifting the original function f(x) with vertex (6, 3) three units to the left and two units up.

Step-by-step explanation:

The question asks about the vertex transformation of a quadratic function when the function is modified. The original quadratic function is given by y=f(x) with a vertex at (6, 3). The transformed function is g(x)=f(x+3)+2. To find the new vertex of g(x), we apply the transformation rules to the original vertex. The function f(x+3) means that the graph of f is shifted 3 units to the left, and the +2 means that the graph is then shifted up by 2 units. Therefore, the new vertex is (6 - 3, 3 + 2) = (3, 5).