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

LiIIiam0216 Aug 11, 2024

#1**+1 **

The maximum possible value of the expression occurs at the vertex of the graph.

So let's find the y value of the vertex.

First, simplifying and combining all like terms, we get the equation

\(4t^{2}+4t+14\)

Now, the x value of the vertex of the graph is \(\frac{-b}{2a}\), so we have

\(\frac{-4}{8} = -1/2\)

Plugging this value back into equation and subbing out t, we get

\(y = 13\)

So 13 is the our answer.

Thanks! :)

NotThatSmart Aug 12, 2024

#2**+1 **

Sorry, just realized, for this question, there IS no max value.

The MIN value is 13 since the parabola open upwards.

My bad.

NotThatSmart
Aug 12, 2024