Question

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

parabola is (3, 5). What is the vertex of the function defined as
g(x) = f(-x) - 3?

Answer 1

Explanation:

f(-x) reflects the original f(x) across the y-axis.

every functional value for a positive x becomes now the functional value of the corresponding negative x. and vice versa.

and f(x) - 3 reduces all the regular functional values by 3.

so, e.g. instead of 5 the y value is then 5-3 = 2.

so, the vertex of g(x) = (-3, 2).

because g(-3) = f(- -3) - 3 = f(3) - 3 = 5 - 3 = 2.

remember, the vertex is a point on the curve and must therefore satisfy the functional expression for the x and y (coordinates) relationship.