I'm trying to create a dataset, and I want data that has, or does not have a parabola. So far, I've been using the quadratic equation by creating random lines $x$ (negative and positive), and random values (negative and positive) for both $a$ and $b$, and I'm getting all of the lines/curves I need.
However, I now want to try and automatically label them and therefore need to be able to create a parabola (or not) without having to manually check them. I understand how $a$ and $b$ in the quadratic equation affect the result, and I think it's the relationship between the line $x$ and the value of $b$ that will determine if there is a parabola or not, but I'm not sure.
Is there a way to control the result I get back?