Answer:
The vertex of g(x) is (6,3).
Step-by-step explanation:
Quadratic Function
The vertex form of the quadratic function has the following equation:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is the leading coefficient.
We know a quadratic function y=f(x) is represented by a parabola whose vertex is at (3,-3). Substituting in the equation:
[tex]y=a(x-3)^2-3[/tex]
The function g(x) is defined as:
[tex]g(x)=-f(x-3)[/tex]
Substituting f(x):
[tex]g(x)=-[a(x-3-3)^2-3][/tex]
Operating:
[tex]g(x)=-a(x-6)^2+3[/tex]
This function is represented by a parabola with its vertex at (6,3).
The vertex of g(x) is (6,3).
