Exploring Quadratic Graphs
The general quadratic function is y=ax2+bx+c
It has one of two basic graphs shapes, as shown below:
It is a symmetrical "U"-shape or "hump"-shape, depending on the sign of a. Another way of saying the same thing is that the y-values drop to a minimum and then rise again if a is poitive, whereas they rise to a maximum and then fall if a is negative.
The roots or solutions of the equation y=ax2+bx+c are given by the intercepts on the x-axis, and by symmetry the maximum or minimum is always halfway between them. Some quadratics equations do not have real roots, and in these cases the graph simply does not cut the x-axis at all.