Quadratic Equation is an equation which contains an x^2 term (or if you want to get technical it is an equation containing a single variable of degree2 with no higher power).

A quad bike with a rat (quadratic) driving, pulling an X-ray (X) of a fish in a square (2) fish tank.

Example 1

A quadratic equation is an equation which contains a x^2 term.

y=x^2

y=x^2+2

y=x^2+x-4

y=x^2+2x-6

All of the equations contain a x^2 term therefore they are called quadratic equations.

Example 2

ax^2+bx+c=0

This is a well known quadratic equation i.e. containing x^2

Example 3

x^2+y^2=z^2

x^3+x^2=0

These are NOT quadratics because the first has another variable with degree squared and the second has one with a higher power than 2.