If you have a quadratic equation, it means you have a variable that is squared or raised to the power of 2. The name comes from quad which means 4. However, there are no powers of 4 in a quadratic equation. Instead, the idea here is that to get the area of a geometric square, you have to square the length of one side. This gives you s^2 or side squared. This gives the area of a 4 sided polygon so equations where the highest exponent is a 2 are called quadratic.
The standard form of a quadratic equation is ax^2 + bx + c = 0. Sometimes you will see it with a y instead of a 0. Normally, you want to solve this equation for the x intercepts which occur when y = 0. Quadratic equations define a smooth curve on the xy plane graphically. Frequently, in algebra you will see these equations in the form of conic sections. The best known are the circle, ellipse, parabola, and hyperbola. If addition variables are introduced, the curves can do a number of differing moves.
Special points on the graphs of quadratic equations are known of as the asymptotes. These are lines that the curve will approach but never touch. These are found on the graph of hyperbola. Also, there are centers on circles, foci on ellipses, and maximums and minimums on parabolas as well as an axis.
Quadratic equations have up to two roots. These may or may not be rational or real numbers. They are usually solved through factoring and the quadratic formula although other techniques can at times be employed such as an array.
