Quadratic Formula - Maple Programming Help

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Quadratic Formula

Main Concept

The solutions of the equation a x2+b x+c=0, where a, b and c are constants with a0, are given by the quadratic formula:

x=b±b24 a c2 a.

Derivation

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

 

0=

a x2+b x+c

 

=

ax2+bax+c

 

=

ax2+bax+b2 a2+cab2 a2

 

=

ax+b2 a2+cb24 a

so

 

 

ax+b2 a2=

b24 ac

 

x+b2 a2=

b24 a2ca

and finally

 

x=

b2 a±b24 a2ca

 

=

b±b24 a c2 a.

 

 

 

 

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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