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

 Aug 1, 2020

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 smiley

 Aug 1, 2020

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

ohh yes sorry I assumed the value was 0 oops

taeijr  Aug 2, 2020

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......

 Aug 2, 2020

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