Ensure the inequality for the parabola is in standard form. For equalities, this would be y = ax^2 + bx + c.
Choose the coordinate range for your graph. To center your graph on the middle of the parabola, set the middle x-coordinate to equal -b/2a, using the "b" and "a" variables from the standard form of the inequality. Find the y-coordinate for the middle of your graph by substituting -b/2a in for x in the equation and solving. Label the x and y axes with their maximum and minimum values.
Select 10 or so values along the x-axis of your graph, evenly spaced. To make a smoother, more accurate curve, choose more values. Calculate the value of y for each x-value by substituting in the x-value into the formula, and plot a point at the corresponding (x, y) position on the graph.
Draw a curve smoothly connecting all of the plotted points in turn. This line represents the solutions for the equation y = ax^2 + bx + c, and is also the boundary for the inequality of the same form. If your equality has a less-than-or-equal-to sign or a greater-than-or-equal-to sign, create a solid line. Otherwise, use a dotted line.
Shade the area above the line from Step 4 if the inequality is of the form, y > ax^2 + bx + c. If the inequality is of the form y < ax^2 + bx +c, shade the area below the line instead.