Question

Which statement about the graph of the function f(x)=2x^2-x-6 are true?

A. The domain of the function is x
B. The range of the function is all real number
C. The vertex of the function is [(1/4)-6(1/8)]
D. The function has two x-intercepts
E. The function is increasing over the interval (-6(1/8), infinity )

Answer 1

c the vertex of the function

Answer 2

C. The vertex of the function is [(1/4)-6(1/8)]

Explanation:

The given function is

`f(x)=2x^(2) -x-6`

This function is a quadratic function.

Its domain is always all real number.

Its range is determined and restricted by its vertex, that is, it can't be all real numbers.

The vertex has coordinates
`(h,k)`, where

`h=-(b)/(2a)`

Having
`a=2, b=-1, c=-6`

Replacing these values, we have

`h=-(b)/(2a)=-(-1)/(2(2))=(1)/(4)`

Then,
`k=f(h)`, that is, we need to replace the value we found

`f(x)=2x^(2) -x-6\\f((1)/(4))=2((1)/(4) )^(2) -(1)/(4)-6=(2)/(16)- (25)/(4)=(2-100)/(16)\\ k=(-98)/(16) =-6(1)/(8)`

Therefore, the right answer is C. The vertex of the function is [(1/4)-6(1/8)]