If we know for a fact that the turning point of a graph is not always exactly between the two $x$-intercepts, I just came across the following
I can use a CAS calculator, but without one, how do I know if the turning point is supposed to be before or after the $y$-axis (I mean the $y$-intercept in this case) if I know that the $x$-intercepts are equidistant from the origin, like $2$ and $-2$
Note that the turning point even in this case is not exactly between the two intercepts even the intercepts themselves are equidistant from the origin.
I think the question is not clear enough. By now I am not even required to find the turning point when sketching, the basics needed are the intercepts and end end behaviour. However, I need an estimate for the turning point, something very rough, like below or above x-axis, just so that the basic shape of the graph is identified.
Again, I do not need to find the turning point, just guess something like in which quadrant would it lie.