Directions: What are the maximum and minimum values for c if x^2 + 12x + 32 = (x+a) (x+b) + c?
2) Try multiplying the binomials. Do you see any relationship between, a,b, and c?
3) Try graphing the function using this: https://www.desmos.com/calculator/4bpceyyd5j
There is no maximum value because the further apart a and b are in value, the higher the value of c to balance the equation. (Allowing a or b to be negative makes the upper limit infinite. For example a =1,000,000 b = -999,988.
As long as the sum is 12.)
Source: Jedidiah Butler