Quadratic Equations

An example of a Quadratic Equation:The name Quadratic comes from "quad" meaning square, because the variable gets

squared (like x2). The Standard Form of a Quadratic Equation looks like this:

a, b and c are known values. a can't be 0. "x" is the variable or unknown.Here are some more examples: -In this one a=2, b=5 and c=3

-This one is a little more tricky:Where is a? In fact a=1, as we don't usually write "1x 2“ b = -3And where is c? Well, c=0, so is not shown.

-Be careful! This one is not a quadratic equation, because it is missing x2 (in other words a=0, and that means it can't be quadratic)

Other example of quadratic form

But sometimes a quadratic equation doesn't look like that! For example:

a, b and c In Standard Form

→In disguise

a=1, b=-3, c=1 x2 - 3x + 1 = 0Move all terms to left hand side

x2 = 3x -1

a=2, b=-4, c=-5 2w2 - 4w - 5 = 0Expand, and move 5 to left

2(w2 - 2w) = 5

a=1, b=-1, c=-3z2 - z - 3 = 0Expand, and move 3 to left

z(z-1) = 3

What Are Quadratic Equations Used for?

There are many every day applications for this type of equation. One of the most useful is calculating rates of acceleration and deceleration, for example, determining the stopping distances for a car traveling at a range of speeds. Another is arriving at the optimum selling price for a product sold by your business, based on costs. This sort of equation can also be used to calculate the area of a geometric figure from its circumference. This makes it invaluable in home decorating, for instance, as when you wish to paint a room and need to calculate its surface area to figure out how much paint you will need to use.