Question

Select the correct answer.

Which point is the vertex of the graph defined by f(x) = 6|x − 2| − 5?

A.
(6, 5)

B.
(2, -5)

C.
(0, 0)

D.
(6, -2)

Answer 1

B. (2,-5)

Explanation:

The vertex of the function can be found in the most lower value that the function can have.

Since we have an ABS function involved we need to analyse it at first

We know that |x| = x if x> 0 and |x| = -x if x< 0

if we now change x by x-2 (the content of our ABS function involved, we have the following

|x-2| = x-2 if x-2> 0

|x-2| = -x+2 if x-2< 0

Those inequaiities have a common solution

x-2=0, this means that x=2 is the lowest value the ABS(X-2) has and it is equals to zero.

So by evaluating x=2 in the given function we will obtain its vertex.

leading to f(2)=6 |2-2|-5= -5

Hence the point (2,-5) is the vertex of our function