Prior to the advent of computers, draftsmen had to use dedicated mechanisms to plot curves. One such instrument was the parabolograph , simulated in this Demonstration and on display in the London Science Museum .
The red pen is connected to a series of bars and sliders. As the pen moves from left to right, it plots the parabola . You can vary the parameter with its slider to move the green bar in the mechanism. You can vary the angle with a slider to rotate the magenta bar.