Use the Quadratic Formula

10.6Solve Quadratic Equations

using the ♫Quadratic Formula ♫

Goal: to learn the quadratic formula, and solve equations using it.

We've solved quadratic equations by factoring --

( )( )x x 5 1 0

We've solved quadratic equations using square roots--

x 2 9

We've graphed quadratic equations and identified the solutions on the graph. y

x

y

x

y

x

How many solutions are shown on each graph?

Try solving:

25 10 2 0x x

What do we do when a quadratic equation doesn’t factor and it can’t be solved using square roots?

We SING!!

…the quadratic formula song. ♫

The quadratic formula can be used to solve ANY quadratic equation that’s written in standard form:

2 0ax bx c

The Quadratic Formula

2 42

b b acx

a

http://www.youtube.com/watch?v=bSQ7nxjmXXg

How does it work?

Put the coefficients of the variables into the formula.

2 0x xba c

2 42

xcb b a

a

Let’s try this equation again:25 10 2 0x x

____ ____ ____a b c 5 10 2

First: what are the values of a, b, and c?

2 0x xba c

____ ____ ____a b c 5 10 2

Next: Replace the letters in the formula with the appropriate number, and then simplify.

2 ( ( ) ) ( ( (

))

)2

4x

10 10 5

5

2

2(10) (10) ( 5)( 5

2)2 )

4 (x

2 410 2 0.15(10) 82 5x

2 410 2 2.15(10) 82 5x

Let’s try another one

2 4 4 0x x

____ ____ ____a b c

What are the values of a, b, and c?

(write it down, work together)

2 0x xba c

2 4 4 0x x ____ ____ ____a b c 1 4 4

2 ( ( ) ) ( ( (

))

)2

4x

Substitute

Simplify

2 4 4 0x x

Notice that we only had 1 solution. Why is that?

Could we ever get no real solution? If so, when?

Before we practice some more…

http://www.youtube.com/watch?v=b1q1pPI79TY&feature=related

On your own:

1. 2. 22 3 5 0x x 2 5 14 0x x a =____

b =____

c =____

a =____

b =____

c =____

Assignment:

pg 674 #4-26 even, 46(Bonus pts for singing the QF song/ reciting the QF.)

Monday – Spirit Day:“Take me out to the ballgame”

Chapter 10 Test: Thurs 3/17