Quadratic equation facts for kids
A quadratic equation is an equation in the form of ax^{2} + bx + c, where a is not equal to 0. It makes a parabola (a "U" shape) when graphed on a coordinate plane.
The Quadratic Formula
The quadratic formula is a formula used to find the points where the graphed equation crosses the xaxis, 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, ax^{2} + bx + c = 0. Also, a cannot be 0 for the formula to work properly.
The factored form of this equation is y = a(x − s)(x − t), where s and t are the zeros, a is a constant, and y and the two xs are ordered pairs which satisfy the equation.
Proof
The quadratic formula is proved by completing the square,
Divide the quadratic equation by a :
Move ^{c}/_{a}:
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:
Which gives:
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 4a^{2}.
Find the square root of both sides.
Move ^{b}/_{2a}: