Solving Quadratic Equations
Factoring
Some Common Factoring Patterns
x^{ 2}  a^{ 2} = (x  a)
Â· (x + a) â€œDifference of two squaresâ€
x^{ 2} + 2 Â· a
Â· x + a^{ 2} = (x + a)^{ 2} â€œPerfect square Iâ€
x^{ 2}  2 Â· a
Â· x + a^{ 2} = (x  a)^{ 2} â€œPerfect square IIâ€
Solving a Quadratic Equation
The objective of solving a quadratic equation:
a Â·
x^{ 2}
+ b
Â·
x +
c =
0,
is to find the values of x
that make the quadratic formula equal to
zero. Graphically, these xvalues
are the xcoordinates
of the points where the graph of
y =
a Â·
x^{ 2}
+ b
Â·
x +
c
crosses the xaxis
(see Figure 2).
When you are trying to solve the quadratic equation
a Â· x^{
2} +
b Â·
x +
c =
0, then what you are trying to do is to find the
xcoordinates
of any points where the graph of y
= a
Â·
x^{ 2}
+ b
Â·
x +
c crosses the
xaxis.
Figure 2: The solutions of a quadratic equation are the
xcoordinates
of the points where the graph of the quadratic cuts through the
xaxis.
