For clarity, I would like to say that the graph in question is "Rising Inflection Graph" as listed here https://mathspace.co/learn/world-of-maths/cubic-functions/find-the-equation-of-a-cubic-function-33836/find-the-equation-1402/.
So what I mean by this is that the graph is the same both ways - i.e the graph follows a negative quadratic pattern until its turning point, where it flips and becomes a positive quadratic of the same graph. How would I find the equation of this?
I was using the Desmos Graphics site, and it seems like the equation I am looking for
y = ax^3 + bx^2 + cx + d
However, I still am at odds as how to find the equation, only given points of the graph.
Non-degenerate cubic polynomials are not piecewise quadratic, so there is no such equation. If you are given the points of a graph, two points uniquely determine a line, three points uniquely determine a quadratic, and four points uniquely determine a cubic. But it won't be two quadratics joined at the hip.