Question

find constants a and b so that the minimum for the parabola f(x) = x^2 +ax+b is given at the point (2,5)

Answer 1

set dy/dx = 0 = 2x +a
x = -a/2 = 2 so a = -4

check (d/dx)(dy/dx) = 2 > 0 so this is a minimum

at (2,5)
f(x) = y = 5 = (2)^2 + (-4)(2) + b = 4-8+b
b = 9

y = x^2 -4x + 9 is answer