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In order to draw a parabola with the function y=a*x^2+b*x+c you must calculate some reference points.

A good place to start is by calculating the vertex and the roots with the formulas explained on the previous sites.

If there is a point of intersection between the graph and the y-axis it can be putted directly into the coordinate system, because the value of c in the quadratic function indicates the point (0,c).

The other reference points should be chosen with appropriate intervals, so it’s as easy as possible to draw the parabola.

The more reference points you have, the more precise you can draw the graph. At least 7 points are needed.

Make a data table and put the values of the reference points into it. Use freehand to draw the graph as a curve passing through the points.

Draw a parabola