Okay, my pre-calculus teacher isn't very good at explaining things. We're working on graphing polynomial functions, and he went on about them. Unfortunately half the class didn't understand a word he said. So, I would like somebody to guide me through a sample problem (please be very specific, and use visual examples; that's how I learn):

y = x^2 - 4x

X^2 is X to the second power, if that helps.

What are you supposed to do? If it is just graphing. Well, whip out the calculator and graph it.

It is a parabola with vertex at (2,-4) and is concave up. If the x^2 term is positive, then it is concave up. If it is negative, then concave down.

We can find the vertex by using

Where a=1 (the coefficient of the leading term) and b=-4 (the coefficient of the linear term or x term).



Plug that back in to find y...

There we go for the vertex.