Find the smallest distance between the graphs y=x^2 - 4x + 12 and y=2x + 1. Thanks for any help
Answer= 0.894427...
The shortest distance will be along the normal to both curves. That is, when the curves are parallel, having equal slopes. The line has constant slope = 2, so we need
2x-4 = 2
x = 3
The normal line through (3,9) with slope -1/2 is
y = -1/2 x + 21/2
which intersects y=2x+1 at (19/5,43/5)
so the distance is √((3-19/5)^2+(9-43/5)^2) = 0.894427