Find m if the line y=mx−2 intersects y=x^2 in just one point.

We have that
y=mx−2
y=x²

if the line intersects a the parabola in one point
so
mx-2=x²-------> x²-mx+2=0
Find the discriminant D=b²-4ac
a=1
b=-m
c=2
D=m²-8
we know that

If D is negative ------> Then the square root is imaginary and there is no solution
If D is 0 then there is exactly one solution
if D is positive there are two solution 
therefore
equals D to zero
m²-8=0-------> m=(+/-)√8

the answer is 
m=(+/-)√8

see the attached figure
m has two solutions