Question

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

Answer 1

C the vertex of the function

Answer 2

Answer:

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

Step-by-step 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

$h=-\frac{b}{2a}$

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

Replacing these values, we have

$h=-\frac{b}{2a}=-\frac{-1}{2(2)}=\frac{1}{4}$

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

$f(x)=2x^{2} -x-6\\f(\frac{1}{4})=2(\frac{1}{4} )^{2} -\frac{1}{4}-6=\frac{2}{16}- \frac{25}{4}=\frac{2-100}{16}\\ k=\frac{-98}{16} =-6\frac{1}{8}$

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