Directions: What are the maximum and minimum values for c if x^2 + 12x + 32 = (x+a) (x+b) + c?
Hint
Hint
1) Can c be positive? Negative? Zero?
2) Try multiplying the binomials. Do you see any relationship betwee, a,b, and c?
3) Try graphing the function using this: https://www.desmos.com/calculator/4bpceyyd5j
Answer
Answer
One of the values can be found by splitting a and b equally as (x+6)(x+6) which gives c=-4. This is the minimum value for c.
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.
Source: Jedidiah Butler