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# Algebra

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What real value of produces the smallest value of the quadratic t^2 - 9t - 36 + 3t^2 - t + 10?

Apr 26, 2022

#1
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The real value of t = 16/3 produces the smallest value.

Apr 27, 2022
#2
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Simplify it to: $$4t^2-10t-26$$

The least possible value occurs at: $$\large {-b \over 2a}$$

The quadratic equation is in the form $$ax^2+bx+c$$ only difference being that we have t instead of x.

Plugging in the values, we have the lowest real value occurs at $$\color{brown}\boxed{5 \over 4}$$

Apr 28, 2022