Consider the curve and the line

MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

Consider the curve

y=-x^2+3x-6

and the line

y=mx-2

. Find the values of

m

for which the line: (a) Meets the curve twice. (b) Is tangent to the curve. (c) Does not meet the curve.