Question

a quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (6,-6) what is the vertex of the function defined as g(x)=f(x+4)

Answer 1

the vertex of g(x) is (2, -6).

Explanation:

To find the vertex of the function g(x) = f(x + 4), we can start by considering the vertex form of a quadratic function:

y = a(x - h)^2 + k

In this form, (h, k) represents the vertex of the parabola.

Given that the vertex of f(x) is (6, -6), we can substitute these values into the vertex form:

y = a(x - 6)^2 - 6

To find the vertex of g(x), we need to substitute x + 4 for x in the equation above:

g(x) = a((x + 4) - 6)^2 - 6

Simplifying this equation, we have:

g(x) = a(x - 2)^2 - 6

So, the vertex of g(x) is (2, -6).