Quadratic Functions

How to identify quadratic functions: 
Standardform: ax² + bx + cy² + dy + e= 0

If you have an equation like 4x² + 4y²=36  The equation is a circle, because a=c
Example of a circle

If a or c equals 0 the equation is a parabola (for example: 2x² + 4y= 3)

Example of a parabola:

If a or c have different signs the equation is a hyperbola ( for example: 4x² - 4y²= 12)

Example of a hyperbola

 If you have an equation like 4x² + 3y²= 25 the equations is an ellipse, because a is not equal to c and the signs are the same
Example of an ellipse