Name: Knowunity
Brand: Knowunity

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Learn how to solve quadratic equations and inequalities using various methods and techniques.

https://content-eu-central-1.knowunity.com/CONTENT/jxwDneHCbnjfbeisacoF.pdf

jxwDneHCbnjfbeisacoF

Study note

Kyra Anderson

United States of America

DEFAULT (US)

Pre-Calculus

Unit 1, sections 1-7 notes

Probability & combinatorics

Permutations

fetersielstwo do
1.1 of in die
Solving quadratic equations FSF Fonte dhe
74
> Factoring
(h. Accom
1x²-7x+12=0 112/
-47-3
(x-3)(x-4)=0
DX-3=0 X-4=0
4343
+4 +4
X=4
P
▷ Square root method
1)(x-7)²2²-6
X-7=+4
DX-7= 4 x-7=-4
D+7+7
+7+7
DIX=11
x=3
▷ Complete the square
2
1x²-6x+8=0
always x²=6x +9 = -819
two
1-62
=9
2
answers
(±)
(#) (x-3)(x-3) = |ar(x-3) =)
L
X-3=1 X-3=-1.
²x = -2
X=4
22x²²+7x-4 = 0
71 (2x² +8x76x-4)=0
2x(x+4)-1(x+4)=0
(2x-1)(x+4)=0
X=1₂ X=4
memorize: (12/1² Perfect
squares: 4,9,16, 25, 36
Graphing cale reset and →+→7 →1→2
Find Os: 2nd trace 2 → move right + left (depends)
1.1 Day !
▷ Quadratic Formula
буроогодавня
1)2x² - 6x + 1 = 0
(36-8)
-(-6) ± √(-6) ²-4 (2) (1)
2(2)
6±1/28 <
6+2√7
4
3+√7
2
1)x²-x-620
(x-3)(x+2) = 0
X=-0
X-3-0
x=3
memorize -(b) ± √(b) ²-4 (a) (c)
2(a)
*
1.1 Summary-Day!
I learned how to solve
quadratic equations.
I use for completing,
음²
▷ Graphing,
1x²2²-8x+15=0
1x²³²-8x+15=4
1.1 Day 2
▷ Solving quadratics inequalities.
the square. I use I taget
-two answers.
Memorize quadratic form.
DE √COX²-4axes split in 2
2(a)
hippyday
4≤X²-X-6 C
2)32+4x<x2-x-6
-X²+x+6-X²+x+6
x15х+6<0
(x+2)(x+3)=0
|X=-2 x=-3
проспербож
1.1 Day 3
More in depth
1x2-x-1220
(x+3)(x-4)=0
x=-30x=4
проопелфабно
2) 4х +2ках
эт ах -ах
84x29x+240
4х2-8x-x+2
24x(x-2)-1(x-2
74x-1)(x-2) =0
х=9 [x=2
a
А
4>x3+5х+6
Агрождоволд
Gurydeng
hippolydong
-45x2-x-12
(0.5, -12.25)
Ч
узиха ах, 2 рис113 13. с.) 321+4x-x²0
(x+7)(x-3)=0
1-x²-3x+7x+21=0²
7-x(x+3) 7(x+3)
(x+3)(x+7)=0
X=-3X=7
продавн
пропусвојо
Grouping
4<-x2+4x+21
1.1 Summary - Day 2+3
I learned how to solve
quadratic inequalities.
2x²+3x-5 (Sorz) line is dotted + (<or>) is
If the sign has a line under
2x2-2x+5x Solid. If sign is facing the y,
if
-2.x (x-1)+5( #'s, shade outside. facing
(2x+5)(x-1) Calculator!
-1/₂
17 √(x+³/4)³² =√15/²/²6
x+3/4 = ± 1
-3/4 3/4
X=\ x=5/₂
(225)
Completing the square
HHH
( 1.1 Day 4
Solving absolute value equations
4
D-2|x-11=-6
-2
x-1=3
X-1=3 x-1=-3
+H
+1 +1
X=-2
прооподож
hyoyqခt
X=41
2)=3-3
=9
X=9 X=-9
3) |x-2/+3=4
DX-21=1
-3-3
2X=2=1 X-2=-1
8X = 3 [X=1
hoidon
-2/x-1/+6 v(1,6)
A
Aposto
= 1-3 v(0₁-3)
y =
вроокусвојо
1
4 = 1x-21-1 V(2₁-1)
24 1.1 Day
Solving Absolute Value Inequalities
11x-21<3
5
X-2=3 x-2--3
+2+2
+2+2
X-5 -1
проополфавж
2/3x+422
•3x+4=2 3x+4= -2
-4
2-4
33x==2= 3x = -6
3
8 X = 2/3 x==2
32 X+2 | > 1/
x+2=5
X=3
X+2
55
= |_ X+²2=15
X+2=-5
XE-1
and
1.1 Summary-Day4+5
I learned how to solve
absolute value equations
inequalities. Don't shade if
-Signor dot/solid. If
inequality, shade + dot/solid.
Inside abs, switches sign,
outside stays same.
If number infront ofx, take out
•+turn to fraction.
41x-21-3
v(2,-3)
hydon
y</3x+41-2 √(²73,-2)
4≤3/x + 7/31-2
koode
Y²121-1 V(-2,-1)
75
WA
1 1.1 Day 6
Interval Notation/
=
1) X> --
2)x≤2
3)0<x<4
4)X <0 or x 23
1
2
IN
(-1,∞)
-2-101 2
(-∞0,2]
[0,4)
D0<x<3
(0,3)
2)x≤-2 orx>1<10 (-00,-21 (1,00)
1.1 Summary-Day 6
I learned interval notation.
If the sign is for the
circle is shaded & is a
bracket. If sign is Lors, the
circle is open and is a
parenthese.
(-∞0,0) or [3,00) 1.1 Day 7
Functions and their behavior
Ex of a function {(1,1), (2,1),(3,1)3
Not a function: {(1,2), (1,3), (1,4)}
1){(2,6), (-3,6), (4,9),(,10)
function
DD: 22,-3,4,13
R: $6,6,9,103
Dy=x²³-3x
function
·1) f(x)=x²+2
D:(-00,00)
▷ Limit the domain
D Denominator of a fraction cannot =0 memorize: no IN
DIf √x, then x20 memorize: no 0 denominator
*²-1
x+4
f(x)=
Df(-x)
f(x) = (x3²-1
-X+4
f(x)=x²-1
-X+4
2)2x+y² = 1
y = ± √1-2x
(0, -1) (0, 1)
Not a function.
2) g(x) = ²16 3)h(x)=√3x-12
X
(x+4)(x-4)
x+4/0 X-40
D:XX-4 X/4
e)-f(x)
f(x)=
2){(2,4) (0,3), (2,6)}
not a function
only top
Xt
X+4
3x-1220
+12 +12
3x212
X24
D:[4,00)
f)f(x+1)
f(x) = (x+1²-1
(x+1)+4
f(x)=x²+2x+1-1
X+1+4
f(x)=x²+2x
X+5
(X+D(x+1)
1 1.1 Day 7
HL-27
1) Find-6)
• positive
3) What is the domain of
4)What is the rape of [3,4]
5) What are the x-intercepts?-,106) What are the y-intercepts? 3
7) How often does the line y 3 intercept the graph? 2 (0,3) (4,3)
8) For what value of does x)-07
1)y=-2x-9
function
4
3)x= √²+4
1.2 Day !
Functions and their properties
∙it a function?
1₂6x)=x²³
Not a function
q
2) Is (2) positive or negative?
Y=0 (-3,0)(6,0) (10,0)
CD: (-∞0,0∞0) DER
R:(-∞∞∞) BER
1.1 Day 7 Summary
I learned functions and
their behaviors. If denominator
is 0, not a function. If I, not
a function. If X, X 20.
DER OF RER X
2X1² = √(x-1)(x+6)
4 €/(x-1) (x+C)
Not a function.
401 = x² +8
Function.
2)f(x)=x²+2x+1
V
D: (-∞0, ∞) or DEIR
R:[0, ∞) or REPRIX ZO
such
that

Unit 1, sections 1-7 notes

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Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

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Unit 1, sections 1-7 notes

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

13 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying