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If $t$ is a real number, what is the maximum possible value of the expression $-t^2 + 8t -4 +5t^2 - 4t + 18$?

 Nov 22, 2023
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If $t$ is a real number, what is the maximum possible value of the expression $-t^2 + 8t -4 +5t^2 - 4t + 18$?  

 

When you combine like terms, you get 4t2 plus some other   

stuff, but the square is all we're interested in for this problem. 

 

The 4t2 indicates that this curve is a parabola that opens  .  

upward.  Since it opens upward, there is no maximum value,   

.

 Nov 22, 2023

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