QUADRATIC FORMULA

2 WAYS TO SOLVE QUADRATIC EQUATIONS

Factoring(x )(x ) = 0

Graphing

But, what if factoring and graphing are not possible??

EXAMPLE #12x2 – 4x – 3 = 0

* can not be factored: (2x )(x )* can not easily be graphed for a solution:

X 2x2 – 4x – 3 = 0

0 -3

1 -5

-1 -1

EXAMPLE #2x2 – 4x – 8 = 0

* can not be factored: (x )(x )* can not easily be graphed for a solution:

X x2 – 4x – 8 = 0

0 -8

1 -11

-1 -3

WHAT DO WE DO??

We use the

QUADRATIC FORMULA

2a4ac2bbx

THE DIFFERENT PARTS OF THE QUADRATIC FORMULA

Standard Form of a Quadratic Equation:ax2 + bx + c = 0

Let’s look at Example #1 to identifythe different parts:

2x2 – 4x – 3 = 0

ax2 + bx + c = 0

a = 2 b = -4 c = -3

LET’S DO EXAMPLE #1

a = 2 b = -4 c = -3

2a4ac2bbx

210±2=x

4102±4=x

440±4=x

424+16±4=x

2(2)(4)(2)(-3)-2(-4)±4=x

2x2 – 4x – 3 = 0

NOW YOU TRY A PROBLEM

a = 2 b = -1 c = -6

2a4ac2bbx -±-=

23-2,=x

47±1=x4

49±1=x

448+1±1=x

2(2)(4)(2)(-6)- 21±1=x

2x2 – x – 6 = 0

SOME PROBLEMS REQUIRE US TO REWRITE THEM IN STANDARD FORM

FIRST

a = 1 b = -4 c = -8

2a4ac2bbx

32±2=x2

34±4=x

248±4=x

232+16±4=x

2(1)(4)(1)(-8)-2(-4)±4=x

x2 – 4x = 8 Rewrite in standard form x2 – 4x - 8 = 0

NOW YOU TRY A PROBLEM

a = 2 b = 5 c = -10

2a4ac2bbx

2x2 = -5x +10 2x2 + 5x – 10Rewrite in standard form

4105±5-=x

480+25±5-=x

2(2))(4)(2)(-10-2(5)±5-=x

HOW ABOUT YOU TRY SOME PROBLEMS ON YOUR OWN NOW…

Try the QUADRATIC FORMULA WORKSHEET QUADRATIC FORMULA WORKSHEET

and then see me to check your answers

LET’S LISTEN TO THAT SONG AGAIN!

2a4ac2bbx

ANY QUESTIONS???

SOME VERSIONS OF THE QUADRATIC FORMULA SONG:http://www.youtube.com/watch?v=U7q5fgGyqxk

http://www.youtube.com/watch?v=D_0vgqi7fU4