How do I sketch a quadratic function on graph paper?

First you need to draw a set of axis and choose a sensible scale, This is detrmined by parts of the equation such as the x and y intercept. Then what we need to do is to make a table of values. We can do X from -5 to 5 or whatever relevant values and then calculate the Y values to go with each X value. We can then plot these points and connect them up with a smooth curve.