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

Answer 1

you want the solution to

mx-2 = x^2

to have a zero discriminant. So, since

x^2 - mx + 2 = 0

has discriminant of

m^2 - 8

I guess that tells you what m is, right? Take a look at

http://www.wolframalpha.com/input/?i=plot+y%3Dx^2,+y%3D%E2%88%9A8+x-2,+y%3D-%E2%88%9A8+x-2

Answer 2

m is equal to plus or minus sqrt8