From the graph of a quadratic equation, you can find:
The roots. These are the points where the graph crosses the x-axis, and is the solution of the quadratic equation when y=0. Usually, there are either two or zero.
The coefficient of the leading term. In the quadratic equation y= ax^2 + bx + c,
the parabola points upward if a is positive, and downward if a is negative.
The vertex. You can find the vertex, or where the two sides of the parabola meet, by looking at the graph.