The Quadratic Formula[change | edit source]
Where the letters are the corresponding numbers of the original equation, ax2 + 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[change | edit source]
The quadratic formula is proved by completing the square,
Divide the quadratic equation by a :
Use the method of completing the square
- To "complete the square" is to find some "k" so that:
- for some y.
Add to both sides of the equation:
Find the square root of both sides.