I know how ""aX^2"" widens or narrows the parabola in a graph, but how does ""bX"" and ""c"" move the vertex on the graph.
It's not easy to understand from the y = a x^2 + b x + c form just how b works with a to determine the axis of symmetry, then how these quantities work with c to determine the y coordinate of the vertex. The rules are simple enough:
the axis of symmetry occurs at x = - b / (2 a) and
the y coordinate of the vertex is obtained by substituting this x into the function.
Why they work is the harder question.
To understand the answer to this question we have to consider the other form of the quadratic, which is
y = a ( x - h)^2 + k.
a is the same for both forms. h and k are the x and y coordinates of the vertex. We will spend a good bit of time in class discussing how h and k affect the graph. In a nutshell:
if x in the function y = a x^2 is replaced by x - h then in any y vs. x table the y values will 'shift down', which corresponds to shifting the graph to the right, by h units and
the y values will all be increased by k.