Does the function y=2x^2-7x+7 crosses the x axis once

Is it true or false??

False

it does not cross

Look at: c - b²/(4a)

This is the y-coordinate of the vertex. It gives a positive result. This means the vertex lies above the x-axis and the plot never crosses.

Discriminant = b^2 - 4ac
= 49 - 56
= -7 < 0 , hence roots are not real, so it does not cross the x-axis.