Embed Size (px)
DESCRIPTION
Lesson on solving quadratic equations using the quadratic formula -- and a song to remember it by.
Citation preview
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
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
