Graphing quadratics involves plotting the graph of a quadratic function, which is typically in the form of y = ax² + bx + c. The graph of a quadratic function is a parabola, which can open either upwards or downwards depending on the value of a. The vertex of the parabola represents the highest or lowest point, while the axis of symmetry divides the parabola into two mirror-image halves. To graph a quadratic, one can find key points such as the vertex, x-intercepts, and y-intercept. The vertex can be calculated using the formula x = -b/(2a). Once these points are plotted, the shape of the parabola can be drawn, illustrating the behavior of the quadratic function across the coordinate plane.