Calculus question

Question

A parabola whose minimum is at (−8,2) has the equation y=x2+ax+b. Find a and b. 

Answer 1

Using calculus, we know the minimum of the parabola is at (-8,2). Therefore, at the minimum the derivative of the function must be zero (0).

f(x) = x² + ax +b

f'(x) = 2x + a = 0

f'(-8) = 2*(-8) + a = 0 --> a = 16

With a now found we can use the evaluation of the function f(x) to solve for b...

f(-8) = (-8)² + 16(-8) + b = 2

64 + -128 + b = 2 --> b = 66

Therefore f(x) = x² +16x + 66