# getting the coordinates

With the given function from a previous problem I was solving link, I want to create/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 $$ax^2+bx+c=y$$. I also want to use the plot command to show this coordinate system with the parabola obtained from it.

$$ax^2 + b+x +c=y$$ goes through all the minimum points for the curves you created

• The function in the linked question does not have a parameter p. Please edit your post and add the correct function. – Rohit Namjoshi Oct 12 '20 at 20:03
• the parameter was changed – computer891 Oct 12 '20 at 21:35
• f[a_, x_] = x^2 - 2*(a - 2)*x + a - 2; Assuming[-7 <= a <= 7, Minimize[{f[a, x], -20 <= x <= 20, -7 <= a <= 7}, x] // Simplify] gives {-6 + 5 a - a^2, {x -> -2 + a}} – Bob Hanlon Oct 13 '20 at 0:04
• yes this was from the link I referenced. It gives the equation of the vertex (x,y), where x is a-2 and y is -6 + 5 a - a^2. As you move the parameter a, the vertex coordinates changes. – computer891 Oct 13 '20 at 4:03
• You are difficult to understand since a x^2 + b x + c == 0  is not a curve as you called it. Is this what you want: tab = Table[{a, a - 2}, {a, -7, 7, 14/20}]  and Solve[{#[[1]] == a, #[[1]]*#[[2]]^2 + b #[[2]] + c == 0}, {a, c, b}][[1]] & /@ tab // Quiet  ? – Akku14 Oct 13 '20 at 6:19