Question

Find constants a and b so that the minimum for the parabola f(x)=x^2+ax+b is at the point (6,7)

Answer 1

To find the minimum, take the derivative of the function and equate to zero:

f(x) = y = x² + ax + b
dy/dx = 2x + a = 0
Substitute x =6:
a = -2x
a = -2(6)
a = -12

Then, substitute x = 6, y = 7 and a = -12 to find b.

7 = (6)² -12(6) + b
7 + 36 = b
b = 43

Thus, a = -12 and b = 43