9t^4 + 6t^2 + 2
the problem is asking for the value of t at which the graph is at it's minimum.
what i did was set t^4 to x^2 and t^2 to x. So that means I have 9x^2 + 6x + 2.
Completing the square and the vertex formula gave me the same answer of -1/3 as x. So setting that equal to t^2 and solving gives me a no solution answer. I tried solving it using the quadratic formula for the hell of it. 36-72 shows up in the radical, which is negative.
So I'm at a loss, my answer comes out to be undefined.
But the answer to the problem (as stated in the back of the book) is x=0. Also when I put it in a graphing calculator the minimum is indeed 2 at t=0.
As far as I know, undefined is not the same as 0. I must be doing something wrong, and I have a feeling that it's something really stupid. Any help is appreciated. Thank you.