What real value of t produces the smallest value of the quadratic t^2 -9t - 36?
t^2 - 9t - 36 factors to (t+3)(t-12).
The smallest value would be -3. Please correct me if I'm wrong or if I misunderstood your question
hmmm... I tried this problem, and I'm not sure -3 is correct... (but nice work!)
I may not be right either, as I too am a human, but what I think OP (as in taejir, not guest) did wrong was assumed that the quadratic equaled to 0. (also, they aren't asking for the smallest real number, but they instead want a real number for t that makes the quadratic as small as possible.
I see that to get the smallest value for the quadratic, play with numbers from the range 0-9 (becaus 9^2 and 9(9) are the same thing), and see which one brings the smallest value.
This may not be the best or quickest way, but that's all I could think of!
(or, you could try completing the square? that usually helps finding the minima and maxima)