I can't seem to find a way to know if a graph starts from below or above. By that I mean what is pictured below (where the graph starts from the top left).
For example, in this graph below where the equation is as in the picture, I know that the x values are 0, 1 and 3 but I'd have thought that the graph would start from the bottom left quadrant due to the fact that the x is positive. Could someone please explain why in this case it starts from the top left and how to know for other similar cases.
Any help is appreciated, thank you.
Let's get a few simple examples.
Notice that odd powers have one behaviour at the ends and even powers have the opposite behaviour. This continues for higher powers.
You want to graph $$ x^2(x-(\text{don't care}))(x-(\text{don't care})) \\ = x^4 + (\text{don't care}) \text{.} $$ So we expect even power behaviour.
This is exactly what we do when the leading coefficient is positive. When it is negative, flip the graphs upside-down.