Main Concept

The solutions of the equation , where $a$, $b$ and $c$ are constants with $a\ne 0$, are given by the quadratic formula:

.

Derivation

The quadratic formula can be derived by the method of completing the square:

  $0=$ $=$ $a\cdot \left({x}^{2}+\frac{b}{a}x\right)+c$ $=$ $=$ so  and finally   $x=$ $=$ .

Click to place the vertex of a parabola and drag the graph to stretch the parabola. The equation, the graph, the roots, and the quadratic formula for the roots will be displayed below.

 $x=$



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