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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
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
