We have a quadratic equation $$y=ax^2+bx+c$$
With roots $\alpha,\beta$
$\alpha\to\infty$ and $\beta$ is a finite number the equation transforms to $$y_1=bx+c$$
$\alpha,\beta\to\infty$ the new equation becomes
I figured out how the equation transforms in the first two cases by tinkering around on a graphing calculator but when I had to prove it rigorously using math I treated as a problem in limits but it looks like a problem in multivariable calculus? Since $a,b,c$ are dependent on each other and I haven't learnt that yet.
Is there some other way to figure out these transformations without using math above High School level?