Quadratic Form Examples

Examples: How to Factor a Quadratic Equation

Example1: Factoring Quadratic Equations with leading coefficient a=1
Let’s solve the Quadratic Equation \( x^2- 6x+8 = 0\) .
The 2 zeros when multiplied have to equal 8.
That could be 8 and 1 or 4 and 2, and their negatives.

Additionally, they have to add to -6 which implies
the 2 zeros must be -4 and -2.

Therefore,
\( x^2- 6x+8 = (x-4)*(x-2) \) .

Finally, the 2 zeros are \( x=4 , x=2 \)
since \( x-4=0 \) yields \( x=4 \) ,
and \( x-2=0 \) yields \( x=2 \) .

Easy, wasn’t it?

Tip: When using the above Quadratic Equation Solver to solve
\(x^2-6x+8=0\) we must enter the 3 coefficients as
\(a=1, b=-6\) and \(c=8\).

Example 2: Factoring Quadratic Equations with leading coefficient a different from 1

We are to solve the Quadratic Equation \( 2x^2- 12x+16 = 0\) .
First divide by 2 to have a leading coefficient coefficient of a=1.
We get \( x^2- 6x+8 = 0\) just like in the above example.

The 2 zeros when multiplied have to equal 8.
That could be 8 and 1 or 4 and 2, and their negatives.

Additionally, they have to add to -6 which implies
the 2 zeros must be -4 and -2.

Therefore,
\( x^2- 6x+8 = (x-4)*(x-2) \) and also
\( 2x^2- 12x+16 = 2*(x-4)*(x-2) \) .

Finally, the 2 zeros are \( x=4 , x=2 \)
since \( x-4=0 \) yields \( x=4 \) ,
and \( x-2=0 \) yields \( x=2 \) .

Get it now?