135 week 12..notebook April 12, 2017 Agenda Review Quiz 11 Complex Numbers Completing the Square Quadratic Formula
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135 week 12..notebook April 12, 2017
Agenda
Review Quiz 11
Complex Numbers
Completing the Square
Quadratic Formula
135 week 12..notebook April 12, 2017
LCD: (v+3)(v+4)
v(v+4) + 9(v+3)=v8
v^2 +4v +9v + 27 v +8 = 0
v^2 +12v +35 = 0
(v + 7)(v + 5) = 0
v = 5, 7 check NOT 3,4
so both work
60(x5) = 10(x+5)
60x 300 = 10x + 50
10x +300 10x +300
50x = 350 x=7
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
32=2*2*2*2*2512=2*2*2*2*2*2*2*2*2
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
200mile
hr
500(200w) = 300(200+w)
100000500w=60000+300w
60000+500w 60000+500w
40000 = 800w
400/8 = 50 = w
135 week 12..notebook April 12, 2017
z
4y + 3
x2x+3 3x4 +10x3 + 0x2 19x 13
135 week 12..notebook April 12, 2017
Factoring to solve an equation
Ex: x + 2 = 0 x = 2
Ex: 4x = 0 x = 0
Ex. (x + 1) ( x 2) = 0 x= 1,2
Ex: x2 + 5x + 6 = 0
factor first
(x + 3)( x + 2) = 0 x = 2,3
Ex: (x 1)2 + 4 = 5
(x 1)2 = 1
| x 1| = 1
x 1 = 1
or
x2 2x + 1 + 4 = 5
x2 2x = 0
x(x2)= 0 x=0,2
EX:
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
Completing the Square
(x 1) 2 x2 2x + 1
(x 5 )2 x2 10x + 25
ex: x2 + 20 x = 144
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
QUADRATIC FORMULA
Ax2 + Bx + C = 0
note: we used completing the square to find the formula
x = B B 4 A C
2A x2+ 20x = 144
x2+20x144=0
x= 20 20 4 (1)(144)
2(1)
A=1
B=20
C=144
AC = 24 <
4w2 + 8w 3w 6
4w (w + 2) 3 (w + 2)
(w + 2) ( 4w 3)
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
Discriminant
Examples
135 week 12..notebook April 12, 2017
( u 9) ( u 1) = 0
u = 9 , 1
y +2 = 9 y + 2 = 1
y = 7 y = 1
135 week 12..notebook April 12, 2017
Project Work
135 week 12..notebook April 12, 2017
135 week 12..notebook April 12, 2017
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