math
posted by mike .
Find the values of a,b, and c if the parabola y=a(x^2)+bx+c is tangent to the line y=2x+3 at (2,1) and has a critical point when x=3

y' = 2ax + b
we want y'(3) = 0, so
6a+b = 0
the line 2x+3 has slope 2, so
we want y'(2) = 2, so
4a+b = 2
and we have (a,b) = (1,6)
y = x^2  6x + c
We know that y(2) = 1, so
1 = 4  12 + c
so, c = 7
y = x^2  6x + 7