What real value of t produces the smallest value of the quadratic t^2 -9t - 36?

Guest Aug 1, 2020

#1**+2 **

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

taeijr Aug 1, 2020

#2**+1 **

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)

:)

ilorty
Aug 2, 2020

#3**+2 **

Smallest value of the function will occur at t = -b/2a where a = 1 b = -9 9/2 = t

put this value of t into the equation to calculate the minimum value of the funtion which occurs at this time......

ElectricPavlov Aug 2, 2020