Quadratic equation
From Simple English Wikipedia, the free encyclopedia
A quadratic equation is an equation in the form of ax2 + bx + c, where a is not equal to 0. It makes a parabola (a "u" shape) when graphed on a coordinate plane.
[edit] The Quadratic Formula
The quadratic formula is a formula used to find the points where the graphed equation crosses the x-axis, or the horizontal axis. These points are called the "zeroes" of a function. The formula is:
Where the letters are the corresponding numbers of the original equation, ax2 + bx + c. a is not 0
[edit] Proof
The quadratic formula is prooved by completing the square,
Divide the quadratic equation by a :
move
Use the method of completing the square
- To "complete the square" is to find some "k" so that:
- for some y.
-
-
- and
-
- so
Add to both sides of the equation:
makes:
The left side is now a perfect square; it is the square of
The right side can be a single fraction, with a common denominator 4a2.
Find the square root of both sides.
move