Let $f(x) = ax^2 + bx + 18$ be a quadratic polynomial. If the minimum value of $f(x) = 6$ when $x = 2$, find $a + b$.
The vertex = ( 2, 6)
The x coordinate of the vertex = -b / ( 2a) = 2
-b = 4a
b = -4a
So....since (2,6) is on the graph we have
6 = a(2)^2 - 4a(2) + 18
6 -18 = 4a - 8a
-12 = -4a
-12/-4 = a = 3
So b = -4(3) = -12
a + b = 3 - 12 = - 9
