To find the minimum of the parabola, the equation must be
derived and equated to zero as follows.
F(x)= [tex] x^{2} [/tex] + ax + b
F'(x) = 2x + a = 0
The minumum is at point (5,7). Thus, we substitute x with 5 to find a.
2(5) + a = 0
a = -10
To find for b, we replace x, y, and a values to the original equation of the parabola as follows.
F(x)= [tex] x^{2} [/tex] + ax + b
y= [tex] x^{2} [/tex] + ax + b
7 = [tex]5^{2} [/tex] + (-10)(5) + b
b = 32
Therefore the answer is: a = -10 and b = 32
