solving Quadratic by Quadratic Formula.ppt

Quadratic Equations are written
in the form ax2
+ bx + c = 0,
where a ≠ 0.

Drill:
Identify the value of a, b and c.
1. x² + 5x + 6 = 0
2. 2x² -12x = 0
3. x² - 27 = 0
4. 2x² - x – 5 = 0

Methods Used to
Solve Quadratic Equations
1. Factoring
2. Square Root Property
3. Completing the Square
4. Quadratic Formula

Why so many methods?
- Some methods will not work for
all equations.
- Variety is the spice of life.
- Some equations are much
easier to solve using a
particular method.

Factoring
Factoring is typically one of the easiest
and quickest ways to solve quadratic
equations;
however,
not all quadratic polynomials can be
factored.
This means that factoring will not work to
solve many quadratic equations.

Factoring (Examples)
Example 1
x2
– 2x – 24 = 0
(x + 4)(x – 6) = 0
x + 4 = 0 x – 6 = 0
x = –4 x = 6
Example 2
x
2
– 8x + 11 = 0
x
2
– 8x + 11 is prime;
therefore, another
method must be
used to solve this
equation.

Square Root Property
This method is also relatively quick and
easy;
however,
it only works for equations in which the
quadratic polynomial is written in the
following form.
x2
= n or (x + c)2
= n

Square Root Property (Examples)
Example 1 Example 2
x2
= 49 (x + 3)2
= 25
x = ± 7 x + 3 = ± 5
x + 3 = 5 x + 3 = –5
x = 2 x = –8
2 49
x  2
( 3) 25
x 
Example 3
x
2
– 5x + 11 = 0
This equation is
not written in the
correct form to
use this method.

Completing the Square
This method will work to solve ALL
quadratic equations;
however,
it is “messy” to solve quadratic equations
by completing the square if a ≠ 1 and/or b is
an odd number.
Completing the square is a great choice for
solving quadratic equations if a = 1 and b is
an even number.

Completing the Square (Examples
Example 2
a ≠ 1, b is not even
3x
2
– 5x + 2 = 0
2 5 2 0
3 3
x x
  
2 5 25 2 25
3 36 3 36
x x
   
2
5 1
6 36
x
 
 
 
 
 
5 1
6 6
x 
5 1
6 6
x  
5 1
6 6
x  
OR
x = 1 OR x = ⅔

Quadratic Formula
This method will work to solve ALL quadratic
equations;
however,
for many equations it takes longer than some
of the methods discussed earlier.
The quadratic formula is a good choice if the
quadratic polynomial cannot be factored, the
equation cannot be written as (x+c)2
= n, or a
is not 1 and/or b is an odd number.

solving Quadratic by Quadratic Formula.ppt

Quadratic Formula (Example)
x2
– 8x – 17 = 0
a = 1
b = –8
c = –17
2
8 ( 8) 4(1)( 17)
2(1)
x
   

8 64 68
2
x
 

8 132
2
x


8 2 33
2
x


4 33


Activity:
Solve the following quadratic Equations
using QUADRATIC FORMULA:
x² + 2x = 35
x² - 2x + 1 = 0
x² + 5x + 6 = 0

solving Quadratic by Quadratic Formula.ppt

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