According to the University of California, San Diego (UCSD), a parabolic curve, or "parabola," is the graphical representation of a quadratic equation. To draw one, the points of a function are plotted on an x-y coordinate grid and the plotted points are connected in succession. The solution should look similar to the bottom half of a circle.
The example that UCSD provides includes the equation f(x) = 3x^2 (to be read as "3x squared"). By first assigning a value of 0 and solving the function, one is able to find the bottom point of the parabola. Since f(x) = y, it is known that when x = 0, so does y (3(0)^2 = 0), resulting in the point (0,0). By increasing the absolute value of x, one moves to the left and the right of the origin (the point where the x and y axis intersect) and vertically along the y-axis.
When one substitutes the increased absolute values for x in the equation, solves for y, plots the point, and connects the plotted points, he is able to draw a parabola. For example, substituting -3 (absolute value 3) into the equation results in a y-value of 9 and the point (-3,9). If a person were to substitute 3 for x, the resulting point would be (3,9). By plotting the three points discussed here and connecting them by a line, it is possible to see the shape of a parabola. It is important to recognize that parabolas have a rounded bottom and not a pointed one like the graph of an absolute value function.