+2653 If $t$ is a real number, what is the maximum possible value of the expression $-t^2 + 8t -4 +5t^2 - 4t + 18$?
+1897 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! :)
+1897 Sorry, just realized, for this question, there IS no max value.
The MIN value is 13 since the parabola open upwards.
My bad.
