Depends on what degree the polynomial is… most commonly used is the qudratic polynomial, ax^2 + bx + c = 0, (ax^2 is the same as a times x squared) which is usually depicted by a parabola which is kind of like a big U. It can also be upside-down if the polynomial is negative. A simple example is a polynomial derived from (x+1)^2 (x plus 1 squared)… which in qudratic form is x^2 + 2x + 1 = 0. Graphed, this equation would have the vertex (lowest point or highest point depending on if its positive or negative, in this case it would be the lowest point) with the point (-1,0) since the original x^2 vertex is (0,0) the equation (x+1)^2 moved it back one because it added 1… to make it more clearer, lets say (x+1)^2 = y… however we want the vertex to be on the x-axis, so why has the value of 0 (zero). Now we solve by taking the root of both sides.. so now x+1=0 and x = -1… you can keep putting in points like this to graph your equation. For example… I want to know a point with the x value of 3… so I plug in 3 for x and solve… (3+1)^2 … (4)^2 = 16, therfore the point is (3,16).

Microsoft Excel has that capability. Just enter data points onto the spread sheet, make a graph, and make a best fit polynomial function.