Part a:
Let's factor f(x)=2x² - x -6
= (x-2)*(2x+3)
Part b: Solve for f(x) = 0
(x-2)*(2x+3) = 0
x-2 = 0
x = 2
OR
2x+3 = 0
2x = -3
x= -3/2
Part C: In a quadratic equation, such as the one given, the line of symmetry is given by:
x = -b/2a
x= -1/2*2
x= - 1/4
Bellow, you can see the graph: