Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first...
-
Upload
shannon-roberts -
Category
Documents
-
view
214 -
download
0
Transcript of Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first...
![Page 1: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/1.jpg)
Monday May 6th 2013
Honors Algebra
![Page 2: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/2.jpg)
May 6th The Quadratic Formula
Why didn’t we learn this first ?
![Page 3: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/3.jpg)
a2
Quadratic Formula
There once a negative boy who was all mixed up so he went to this radical party. Because the boy was square, he lost out on 4 awesome chicks so he cried his way home when it was all over at 2 AM.
b 2b ac4x
![Page 4: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/4.jpg)
Quadratic Formula
a
acbbx
2
42
02 cbxax
IF
THEN
![Page 5: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/5.jpg)
THE QUADRATIC FORMULA
1. When you solve using completing the square on the general formula you get:
2. This is the quadratic formula!3. Just identify a, b, and c then substitute
into the formula.
2 4
2
b b acx
a
2 0ax bx c
![Page 6: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/6.jpg)
WHY USE THE QUADRATIC FORMULA?
The quadratic formula allows you to solve
ANY quadratic equation, even if you
cannot factor it.
An important piece of the quadratic formula
is what’s under the radical:
b2 – 4ac
This piece is called the discriminant.
![Page 7: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/7.jpg)
WHY IS THE DISCRIMINANT IMPORTANT?
The discriminant tells you the number and types of answers (roots) you will get. The discriminant can be +, –, or 0 which actually tells you a lot! Since the discriminant is under a radical, think about what it means if you have a positive or negative number or 0 under the radical.
![Page 8: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/8.jpg)
WHAT THE DISCRIMINANT TELLS YOU!
Value of the Discriminant
Nature of the Solutions
Negative 2 imaginary solutions
Zero 1 Real SolutionPositive – perfect
square2 Reals- Rational
Positive – non-perfect square
2 Reals- Irrational
![Page 9: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/9.jpg)
Understanding the discriminantDiscriminant
acb 42 # of real roots
042 acb 2 real roots
042 acb 1 real roots
042 acb No real roots
![Page 10: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/10.jpg)
#1 Solve using the quadratic formula.0273 2 xx
a
acbbx
2
42
2 ,7 ,3 cba
)3(2
)2)(3(4)7()7( 2 x
6
24497 x
6
57 x
6
12x
6
2x
3
1 ,2x
6
257 x
![Page 11: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/11.jpg)
#2 Solve using the quadratic formula542 2 xx
a
acbbx
2
42
5 ,4 ,2 cba
)2(2
)5)(2(4)4()4( 2 x
4
40164 x
4
564 x
4
1424 x
0542 2 xx
2
141x
9.2x 9.0x
4
1444 x
![Page 12: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/12.jpg)
Solve using the quadratic formula3.
4.
5.
752 xx
mm 1083 2
ix2
3
2
5
3
2 ,4 m
xx 16642 8x
![Page 13: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/13.jpg)
#3 Solve using the quadratic formula 752 xx
a
acbbx
2
42
7 ,5 ,1 cba
)1(2
)7)(1(455 2 x
2
28255 x
2
35 x
ix2
3
2
5
0752 xx
ix2
3
2
5
![Page 14: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/14.jpg)
#4 Solve using the quadratic formula mm 1083 2
a
acbbm
2
42
8 ,10 ,3 cba
)3(2
)8)(3(4)10()10( 2 m
6
9610010 m
6
1410 m
6
24m
6
4m
3
2 ,4 m
08103 2 mm
6
19610 m
![Page 15: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/15.jpg)
#5 Solve using the quadratic formula xx 16642
a
acbbx
2
42
64 ,16 ,1 cba
)1(2
)64)(1(41616 2 x
2
25625616 x
2
016 x
8x
064162 xx
![Page 16: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/16.jpg)
2
2
2
2
2
1. 2 63 0
2. 8 84 0
3. 5 24 0
4. 7 13 0
5. 3 5 6 0
x x
x x
x x
x x
x x
1. 9,7
2.(6, 14)
3. 3,8
7 34.
2
5 475.
6
i
i
![Page 17: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/17.jpg)
The Discriminant
Discriminant In the quadratic formula, the expression underneath the radical that describes the nature of the roots.
![Page 18: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/18.jpg)
Understanding the discriminantDiscriminant
acb 42 # of real roots
042 acb 2 real roots
042 acb 1 real roots
042 acb No real roots
![Page 19: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/19.jpg)
#6 Using the discriminant0134 2 yy
acb 4 nt discrimina 2
1 ,3 ,4 cba
)1)(4(4)3( nt discrimina 2
169 nt discrimina
52 nt discrimina
052
roots real 2
![Page 20: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/20.jpg)
0134 2 yy
542 2 xx
484 2 xx
1)2)3)
![Page 21: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/21.jpg)
#7 Using the discriminant54 2 xx
acb 4 nt discrimina 2
5 ,1 ,4 cba
)5)(4(4)1( nt discrimina 2
801 nt discrimina
79 nt discrimina
079
roots real 0
![Page 22: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/22.jpg)
Using the discriminant
8.
9.
542 2 xx
484 2 xx
56nt discrimina
roots real 2
0 nt discrimina
root real 1
![Page 23: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/23.jpg)
#8 Using the discriminant
542 2 xx
acb 4 nt discrimina 2
0542 2 xx
)5)(2(4)4( nt discrimina 2
4061 nt discrimina
56nt discrimina
056
roots real 2
![Page 24: Monday May 6 th 2013 Honors Algebra. May 6 th The Quadratic Formula Why didn’t we learn this first ?](https://reader035.fdocuments.net/reader035/viewer/2022081603/56649de75503460f94ae16ff/html5/thumbnails/24.jpg)
#9 Using the discriminant484 2 xx
acb 4 nt discrimina 2
0484 2 xx
)4)(4(4)8( nt discrimina 2
6446 nt discrimina
0 nt discrimina
00
root real 1