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.
this is way over MY head as well as way over anything in the text book. what you posted above is completely foreign.
The only tools that this class has provided is the vertex formula and completing the square for minimums. And also changing equations that are closely related to a quadratic into a quadratic. For example x^4 + x^2 + c into t^2 + t + c. Then setting what you find in the quadratic equation equal to the x^2 in the original. For example t=x^2. 3=x^2. root 3=x.