Question

The quadratic function f(x) has a turning point at (-3,8). if the function g is defined by g(x)=-f(x+5) for all values of x then at which of the following points will g(x) have a turning point?

(1) (-8,-8)
(2) (5,-3)
(3) (8,-8)
(4) (-2,8)​

Answer 1

(-8,-8)

Explanation:

We have that f(x) has a guy point at (-3,8).

If the function g is defined as:

`g(x) = - f(x + 5)`

then we want to find the turning point of g(x).

Note that from the above transformation, g is obtained by shifting f to the left, 5 units.

This will move the vertex to (-8,8).

This is then followed by a reflection in the x-axis.

The new vertex will be at;(-8,-8)