How do you recognize the graph from an equation?

Answer 1

Sometimes you just have to take the trouble to do the actual graphing, since the results can often be quite unexpected.

On the other hand, you should learn to recognize some common forms, including (I'll use the symbol "^" for power):

y = ax + b, with constants a and b - a straight line.

• ax + by = c, constants a, b, and c - also a straight line.
• x^2 + y^2 = a, for any constant a, is a circle.
• y = ax^2 + bx + c, constants a, b, and c - a parabola.

  Some knowledge of calculus can help in the analysis of the form of an equation. For example, if you know how to take derivatives you can find candidates for maximum and minimum values, see where a curve will be convex or concave.