Answer:
Step-by-step explanation:
The function is f(x)=x^2 + ax + b
Derivate the function:
● f'(x)= 2x + a
Solve the equation f'(x)=0 to find a
The minimum is at (3,9)
Replace x with 9
● 0 = 2×3 + a
● 0 = 6 + a
● a = -6
So the value of a is -6
Hence the equation is x^2 -6x+b
We have a khown point at (3,9)
● 9 = 3^2 -6×3 +b
● 9 = 9 -18 + b
● 9 = -9 +b
● b = 18
So the equation is x^2-6x+18
Verify by graphing the function.
The vetex is (3,9) and it is a minimum so the equation is right
