Answer:
Step-by-step explanation:
The given function is
[tex]f(x)=2x^{2} -x-6[/tex]
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 [tex](h,k)[/tex], where
[tex]h=-\frac{b}{2a}[/tex]
Having [tex]a=2, b=-1, c=-6[/tex]
Replacing these values, we have
[tex]h=-\frac{b}{2a}=-\frac{-1}{2(2)}=\frac{1}{4}[/tex]
Then, [tex]k=f(h)[/tex], that is, we need to replace the value we found
[tex]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}[/tex]
Therefore, the right answer is C. The vertex of the function is [(1/4)-6(1/8)]
