High School Do Parabolas and Other Non-Linear Graphs Have Slope?

[DS2C]

So the slope is of course a ratio of the change in y-coordinates to the change in x-coordinates. This is easy to see with a linear equation.
I just came across a cool math simulator ( https://phet.colorado.edu/sims/equation-grapher/equation-grapher_en.html), and I left the first value (ax^2) alone and messed with the other two, which acted as a normal linear equation because the x^2 value was 0.
But when the x^2 term is a non-zero value, and you change the values of b, the graph gets weird and starts tilting. Is this still the slope changing? Does every graph of every power have slope? I'm having a hard time picturing the slope of a parabola.

 

[mfb]

You can determine the slope at a specific x-value. This is possible for every polynomial and for many other functions as well. It is called the derivative of the function. The derivative of ax²+bx+c is 2ax+b. As you can see, it depends on x. As an example, the slope is zero at x=-b/(2a). At this point the parabola has its minimum or maximum.

 

[DS2C]

Ah ok that makes more sense. Thank you.

 

[Integral]

What mfb didn't mention is that the slope is that of a tangent line to function at that point. Thus varies point to point depending on the functionl