Where does the graph of y=2x2-x-3 cross as the x-axis?

This can be determined by finding the x-intercept. In doing so, we let y=0 to find the value of x.

y = 2x^2 - x - 3

[0 = 2x^2 - x-3]:2

0 = x^2 - 1/2 x - 3/2

Complete the squares:

1/16 + 3/2 = x^2 - 1/2x + 1/16

25/16 = (x - 1/4) ^2

sqrt (25/16) = x - 1/4

+ / - 5/4 = x - 1/4

Thus,

x = 1/4 + 5/4 = 3/2

x = 1/4 - 5/4 = - 1

Thus, the graph crosses at x = 3/2 and x = - 1.