Regina S. answered • 11/16/19
Secondary Math Tutor
We have three unknowns so we want to think about this like a system of equations and since we need three values, we should expect three equations to help us.
The first piece of information about the minimum, through a calculus lens, can be interpreted as the derivative would be zero when x=12. Mins and maxs occur where we have a horizontal tangent line, meaning the derivative or slope would be zero. So our derivative would by y'=2ax+b and we can substitute zero for y and 12 for x, 0=2a(12)+b. This is the first of our system of three equations and luckily, it only contains two variables and is easily solved for b if you want to solve the system by substitution.
The other points that the curve goes through will give us the other two equations needed for our system.
0=a(2)^2+b(2)+c and -3=a(1)^2+b(1)+c. Once you substitute the expression for b into both of these, it becomes a more basic system in terms of a and c which should be familiar from Algebra. Let me know if that helps or if you need more explanation.
Regina S.
I see your concern. Based on a minimum at x=12, we would expect it to be increasing as x<12 but the points (2,0) and (1,-3) contradict that trend. Based on the answers you got above, it results in a maximum at x=12 rather than a minimum. So there is definitely a typo in the question, either with a sign somewhere or it should have specified a maximum at x=1211/16/19
Trr R.
Thank you for the reply and time. If I am not mistaken A is - 1/7 B is 24/7 and C is - 44/7.11/16/19