This is something we learned in class to shorten time when you find the sketch of a graph. If the graph its self is not necessary using the discriminant formula will save you time. You must be warned though, it is not a complete short cut, it will only tell you what kind of graph it is.

*Your graph will not need to be in standard form (yay!). This formula will give you the shape of the graph : B^2-4AC. You identify the ABC in the equation and just simply plug into formula. Heres an example of how to do that
x^2+3xy+x^2=4
A=1 B=3 C=2

*Then take those numbers and plug them into an equation. Once you do that you will have to solve it for a single answer.
3^2-4(1)(2)
Simplify
9-8=1
Your answer is 1

*Then aplly your answer to these rules:
~If it is a circle your answer will be a -# and A=C & B=0
~If it is an ellipse your answer will be a -# and A wont =C & B wont =0
~If it is a parabola your answer will be 0
~If it is a hyperbola your answer will be +

*Take your answer and see what it is. The example is a hyperbola.

THE END