I had to redo the problem because there was a mistake. With the given function from a previous problem, I was solving link, I found that the parabola created a trajectory on the graph, ie another parabola.
I'm trying to create a plot where I collect the coordinate points of Min. value for 21 values of parameter a (from -7 to 7), and find a,b, and c such that the points are on the curve of the quadratic equation $ax^2+bx+c=y$. The plot looks something like this
The curve of $ax^2 + b+x +c=y$ goes through all the minimum points for the curves created