Question

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting

parabola is ( 3, -3 ). What is the vertex of the function defined as g(x) = -f (x – 3)

Answer 1

The vertex of g(x) is (6,3).

Explanation:

Quadratic Function

The vertex form of the quadratic function has the following equation:

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

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:

`y=a(x-3)^2-3`

The function g(x) is defined as:

`g(x)=-f(x-3)`

Substituting f(x):

`g(x)=-[a(x-3-3)^2-3]`

Operating:

`g(x)=-a(x-6)^2+3`

This function is represented by a parabola with its vertex at (6,3).

The vertex of g(x) is (6,3).