The quadratic formula is x=-b±√b^2-4ac divided by 2a.
You can only use this formula to solve the quadratic equation: ax^2+bx+c=0
If you were to punch the quadratic formula in the calculator, you would have to punch in the formula except replace the variables with the numbers from the equation.
Ex. x^2+2x+1=0
a=1; b=2; c=1
In the calculator you would punch in x=-2±√2^2-4(1)(1)
Or simply the equation without x=
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This formula is called the quadratic formula.
The quadratic formula is derived by completing the square. That is as much as I can tell you.
In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
The quadratic formula can be derived by used a method called completing the square. It's like using algebra to solve for x. The process is explained the related link "Derivation of Quadratic Formula".
A quadratic equation.