Loading...
3d 2
Save Copy
Desmos Logo
Log In
Sign Up
Expression 15: "M" Subscript, "i" "r" "r" "o" "r" , Baseline left parenthesis, "p" , right parenthesis equals join left parenthesis, "p" , negative left parenthesis, "p" minus "c" Subscript, "e" "n" "t" "e" "r" , Baseline , right parenthesis plus "c" Subscript, "e" "n" "t" "e" "r" , Baseline , right parenthesis
M
i
r
r
o
r
p
=
j
o
i
n
p
,
−
p
−
c
e
n
t
e
r
+
c
e
n
t
e
r
15
Expression 16: "x" less than "x" plus 1
x
<
x
+
1
16
Hidden Label: "P" Subscript, "r" "o" "j" , Baseline left parenthesis, "q" Subscript, 2 , Baseline , right parenthesis
P
r
o
j
q
2
Label
equals
=
undefined
left parenthesis, 4.0 3 3 , 1.3 5 6 , right parenthesis
4
.
0
3
3
,
1
.
3
5
6
left parenthesis, negative 7345 , 717.9 , right parenthesis
−
7
3
4
5
,
7
1
7
.
9
left parenthesis, negative 5.7 7 , 0.1 2 1 3 , right parenthesis
−
5
.
7
7
,
0
.
1
2
1
3
left parenthesis, negative 19.6 7 , 21.3 1 , right parenthesis
−
1
9
.
6
7
,
2
1
.
3
1
undefined
left parenthesis, negative 6.6 2 4 , 1.6 2 6 , right parenthesis
−
6
.
6
2
4
,
1
.
6
2
6
left parenthesis, negative 0.7 9 8 9 , 0.8 3 4 9 , right parenthesis
−
0
.
7
9
8
9
,
0
.
8
3
4
9
undefined
left parenthesis, negative 1.8 7 9 , negative 2.4 4 6 , right parenthesis
−
1
.
8
7
9
,
−
2
.
4
4
6
left parenthesis, negative 0.9 6 2 6 , negative 1.1 2 , right parenthesis
−
0
.
9
6
2
6
,
−
1
.
1
2
left parenthesis, negative 1.9 5 7 , negative 50.2 3 , right parenthesis
−
1
.
9
5
7
,
−
5
0
.
2
3
left parenthesis, 0.1 3 1 7 , 2.4 3 3 , right parenthesis
0
.
1
3
1
7
,
2
.
4
3
3
left parenthesis, 0.4 3 8 , 1.0 7 2 , right parenthesis
0
.
4
3
8
,
1
.
0
7
2
left parenthesis, negative 4.0 9 7 , 548.3 , right parenthesis
−
4
.
0
9
7
,
5
4
8
.
3
500 element list
17
Hidden Label: "P" Subscript, "r" "o" "j" , Baseline left parenthesis, "M" Subscript, "i" "r" "r" "o" "r" , Baseline left parenthesis, "p" Subscript, 1 , Baseline , right parenthesis , right parenthesis
P
r
o
j
M
i
r
r
o
r
p
1
Label
equals
=
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, negative 0.0 3 0 9 6 , 0.0 2 1 1 8 , right parenthesis
−
0
.
0
3
0
9
6
,
0
.
0
2
1
1
8
left parenthesis, negative 0.0 6 2 5 1 , 0.0 4 1 0 5 , right parenthesis
−
0
.
0
6
2
5
1
,
0
.
0
4
1
0
5
left parenthesis, negative 0.0 9 4 4 8 , 0.0 5 9 5 4 , right parenthesis
−
0
.
0
9
4
4
8
,
0
.
0
5
9
5
4
left parenthesis, negative 0.1 2 6 7 , 0.0 7 6 6 7 , right parenthesis
−
0
.
1
2
6
7
,
0
.
0
7
6
6
7
left parenthesis, negative 0.1 5 8 8 , 0.0 9 2 5 2 , right parenthesis
−
0
.
1
5
8
8
,
0
.
0
9
2
5
2
left parenthesis, negative 0.1 9 0 6 , 0.1 0 7 2 , right parenthesis
−
0
.
1
9
0
6
,
0
.
1
0
7
2
left parenthesis, negative 0.2 2 1 8 , 0.1 2 1 1 , right parenthesis
−
0
.
2
2
1
8
,
0
.
1
2
1
1
left parenthesis, negative 0.2 5 2 1 , 0.1 3 4 3 , right parenthesis
−
0
.
2
5
2
1
,
0
.
1
3
4
3
left parenthesis, negative 0.2 8 1 3 , 0.1 4 7 1 , right parenthesis
−
0
.
2
8
1
3
,
0
.
1
4
7
1
left parenthesis, negative 0.3 0 9 , 0.1 6 , right parenthesis
−
0
.
3
0
9
,
0
.
1
6
left parenthesis, negative 0.3 3 5 2 , 0.1 7 3 3 , right parenthesis
−
0
.
3
3
5
2
,
0
.
1
7
3
3
left parenthesis, negative 0.3 5 9 8 , 0.1 8 7 4 , right parenthesis
−
0
.
3
5
9
8
,
0
.
1
8
7
4
left parenthesis, negative 0.3 8 2 7 , 0.2 0 2 4 , right parenthesis
−
0
.
3
8
2
7
,
0
.
2
0
2
4
left parenthesis, negative 0.4 0 4 , 0.2 1 8 8 , right parenthesis
−
0
.
4
0
4
,
0
.
2
1
8
8
632 element list
18
Hidden Label: "P" Subscript, "r" "o" "j" , Baseline left parenthesis, "M" Subscript, "i" "r" "r" "o" "r" , Baseline left parenthesis, "p" Subscript, 2 , Baseline , right parenthesis , right parenthesis
P
r
o
j
M
i
r
r
o
r
p
2
Label
equals
=
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, negative 0.0 6 1 7 1 , 0.0 4 2 2 2 , right parenthesis
−
0
.
0
6
1
7
1
,
0
.
0
4
2
2
2
left parenthesis, negative 0.1 2 4 2 , 0.0 8 1 5 5 , right parenthesis
−
0
.
1
2
4
2
,
0
.
0
8
1
5
5
left parenthesis, negative 0.1 8 7 1 , 0.1 1 7 9 , right parenthesis
−
0
.
1
8
7
1
,
0
.
1
1
7
9
left parenthesis, negative 0.2 4 9 9 , 0.1 5 1 3 , right parenthesis
−
0
.
2
4
9
9
,
0
.
1
5
1
3
left parenthesis, negative 0.3 1 2 2 , 0.1 8 1 9 , right parenthesis
−
0
.
3
1
2
2
,
0
.
1
8
1
9
left parenthesis, negative 0.3 7 3 2 , 0.2 1 , right parenthesis
−
0
.
3
7
3
2
,
0
.
2
1
left parenthesis, negative 0.4 3 2 5 , 0.2 3 6 , right parenthesis
−
0
.
4
3
2
5
,
0
.
2
3
6
left parenthesis, negative 0.4 8 9 4 , 0.2 6 0 6 , right parenthesis
−
0
.
4
8
9
4
,
0
.
2
6
0
6
left parenthesis, negative 0.5 4 3 3 , 0.2 8 4 2 , right parenthesis
−
0
.
5
4
3
3
,
0
.
2
8
4
2
left parenthesis, negative 0.5 9 3 9 , 0.3 0 7 6 , right parenthesis
−
0
.
5
9
3
9
,
0
.
3
0
7
6
left parenthesis, negative 0.6 4 0 9 , 0.3 3 1 4 , right parenthesis
−
0
.
6
4
0
9
,
0
.
3
3
1
4
left parenthesis, negative 0.6 8 4 2 , 0.3 5 6 3 , right parenthesis
−
0
.
6
8
4
2
,
0
.
3
5
6
3
left parenthesis, negative 0.7 2 3 7 , 0.3 8 2 8 , right parenthesis
−
0
.
7
2
3
7
,
0
.
3
8
2
8
left parenthesis, negative 0.7 5 9 8 , 0.4 1 1 6 , right parenthesis
−
0
.
7
5
9
8
,
0
.
4
1
1
6
632 element list
19
Hidden Label: "P" Subscript, "r" "o" "j" , Baseline left parenthesis, "M" Subscript, "i" "r" "r" "o" "r" , Baseline left parenthesis, "p" Subscript, 3 , Baseline , right parenthesis , right parenthesis
P
r
o
j
M
i
r
r
o
r
p
3
Label
equals
=
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, negative 0.0 9 2 2 5 , 0.0 6 3 1 1 , right parenthesis
−
0
.
0
9
2
2
5
,
0
.
0
6
3
1
1
left parenthesis, negative 0.1 8 5 , 0.1 2 1 5 , right parenthesis
−
0
.
1
8
5
,
0
.
1
2
1
5
left parenthesis, negative 0.2 7 7 8 , 0.1 7 5 1 , right parenthesis
−
0
.
2
7
7
8
,
0
.
1
7
5
1
left parenthesis, negative 0.3 6 9 9 , 0.2 2 3 9 , right parenthesis
−
0
.
3
6
9
9
,
0
.
2
2
3
9
left parenthesis, negative 0.4 6 0 3 , 0.2 6 8 2 , right parenthesis
−
0
.
4
6
0
3
,
0
.
2
6
8
2
left parenthesis, negative 0.5 4 8 3 , 0.3 0 8 5 , right parenthesis
−
0
.
5
4
8
3
,
0
.
3
0
8
5
left parenthesis, negative 0.6 3 2 8 , 0.3 4 5 4 , right parenthesis
−
0
.
6
3
2
8
,
0
.
3
4
5
4
left parenthesis, negative 0.7 1 3 , 0.3 7 9 7 , right parenthesis
−
0
.
7
1
3
,
0
.
3
7
9
7
left parenthesis, negative 0.7 8 8 , 0.4 1 2 2 , right parenthesis
−
0
.
7
8
8
,
0
.
4
1
2
2
left parenthesis, negative 0.8 5 7 4 , 0.4 4 4 1 , right parenthesis
−
0
.
8
5
7
4
,
0
.
4
4
4
1
left parenthesis, negative 0.9 2 0 8 , 0.4 7 6 1 , right parenthesis
−
0
.
9
2
0
8
,
0
.
4
7
6
1
left parenthesis, negative 0.9 7 8 1 , 0.5 0 9 3 , right parenthesis
−
0
.
9
7
8
1
,
0
.
5
0
9
3
left parenthesis, negative 1.0 3 , 0.5 4 4 6 , right parenthesis
−
1
.
0
3
,
0
.
5
4
4
6
left parenthesis, negative 1.0 7 6 , 0.5 8 2 6 , right parenthesis
−
1
.
0
7
6
,
0
.
5
8
2
6
632 element list
20
Hidden Label: "P" Subscript, "r" "o" "j" , Baseline left parenthesis, "q" Subscript, 1 , Baseline , right parenthesis
P
r
o
j
q
1
Label
equals
=
left parenthesis, negative 0.7 4 0 2 , negative 0.8 8 8 , right parenthesis
−
0
.
7
4
0
2
,
−
0
.
8
8
8
left parenthesis, negative 1.1 2 6 , negative 0.9 8 7 , right parenthesis
−
1
.
1
2
6
,
−
0
.
9
8
7
left parenthesis, negative 0.5 6 5 , 0.7 6 8 3 , right parenthesis
−
0
.
5
6
5
,
0
.
7
6
8
3
left parenthesis, negative 0.2 3 8 9 , 1.2 1 1 , right parenthesis
−
0
.
2
3
8
9
,
1
.
2
1
1
left parenthesis, 0.3 4 0 5 , negative 0.2 4 5 4 , right parenthesis
0
.
3
4
0
5
,
−
0
.
2
4
5
4
left parenthesis, 0.5 1 1 4 , 0.5 6 3 1 , right parenthesis
0
.
5
1
1
4
,
0
.
5
6
3
1
left parenthesis, 0.4 4 7 6 , 0.8 7 5 9 , right parenthesis
0
.
4
4
7
6
,
0
.
8
7
5
9
left parenthesis, negative 0.5 3 4 8 , 0.6 9 3 , right parenthesis
−
0
.
5
3
4
8
,
0
.
6
9
3
left parenthesis, negative 0.6 9 8 , negative 0.9 0 9 7 , right parenthesis
−
0
.
6
9
8
,
−
0
.
9
0
9
7
left parenthesis, 0.8 2 0 6 , 1.2 2 9 , right parenthesis
0
.
8
2
0
6
,
1
.
2
2
9
left parenthesis, 0.1 4 3 5 , 0.7 9 1 9 , right parenthesis
0
.
1
4
3
5
,
0
.
7
9
1
9
left parenthesis, negative 0.5 4 6 4 , negative 1.1 5 4 , right parenthesis
−
0
.
5
4
6
4
,
−
1
.
1
5
4
left parenthesis, 0.0 9 5 3 6 , negative 0.6 6 3 7 , right parenthesis
0
.
0
9
5
3
6
,
−
0
.
6
6
3
7
left parenthesis, negative 1.1 8 1 , negative 0.9 0 4 6 , right parenthesis
−
1
.
1
8
1
,
−
0
.
9
0
4
6
left parenthesis, 0.3 3 7 9 , negative 0.3 1 1 6 , right parenthesis
0
.
3
3
7
9
,
−
0
.
3
1
1
6
63 element list
21
Hidden Label: "P" Subscript, "r" "o" "j" , Baseline left parenthesis, "q" Subscript, 3 , Baseline , right parenthesis
P
r
o
j
q
3
Label
equals
=
left parenthesis, 2.0 4 8 , 1.2 4 7 , right parenthesis
2
.
0
4
8
,
1
.
2
4
7
left parenthesis, 4.6 6 9 , 1.9 0 4 , right parenthesis
4
.
6
6
9
,
1
.
9
0
4
left parenthesis, negative 1.0 2 , negative 1.6 2 8 , right parenthesis
−
1
.
0
2
,
−
1
.
6
2
8
left parenthesis, 0.7 9 7 9 , 0.0 1 6 2 5 , right parenthesis
0
.
7
9
7
9
,
0
.
0
1
6
2
5
left parenthesis, negative 1.7 3 3 , negative 2.2 9 , right parenthesis
−
1
.
7
3
3
,
−
2
.
2
9
left parenthesis, 1.5 0 6 , 0.0 9 5 9 8 , right parenthesis
1
.
5
0
6
,
0
.
0
9
5
9
8
left parenthesis, 0.3 1 9 5 , negative 1.7 8 5 , right parenthesis
0
.
3
1
9
5
,
−
1
.
7
8
5
left parenthesis, 1.0 2 5 , negative 0.1 5 9 9 , right parenthesis
1
.
0
2
5
,
−
0
.
1
5
9
9
left parenthesis, negative 3.0 1 3 , negative 1.9 1 1 , right parenthesis
−
3
.
0
1
3
,
−
1
.
9
1
1
left parenthesis, negative 0.2 3 6 2 , negative 0.0 7 1 , right parenthesis
−
0
.
2
3
6
2
,
−
0
.
0
7
1
left parenthesis, negative 5.5 8 9 , 4.6 7 9 , right parenthesis
−
5
.
5
8
9
,
4
.
6
7
9
left parenthesis, negative 2.6 4 , negative 0.0 5 9 7 2 , right parenthesis
−
2
.
6
4
,
−
0
.
0
5
9
7
2
left parenthesis, 2.0 1 , negative 2.6 4 6 , right parenthesis
2
.
0
1
,
−
2
.
6
4
6
left parenthesis, negative 0.2 8 9 7 , negative 1.0 6 4 , right parenthesis
−
0
.
2
8
9
7
,
−
1
.
0
6
4
left parenthesis, negative 2.9 3 5 , negative 2.8 6 4 , right parenthesis
−
2
.
9
3
5
,
−
2
.
8
6
4
63 element list
22
Hidden Label: "P" Subscript, "r" "o" "j" , Baseline left parenthesis, "q" Subscript, 3 , Baseline , right parenthesis
P
r
o
j
q
3
Label
equals
=
left parenthesis, 2.0 4 8 , 1.2 4 7 , right parenthesis
2
.
0
4
8
,
1
.
2
4
7
left parenthesis, 4.6 6 9 , 1.9 0 4 , right parenthesis
4
.
6
6
9
,
1
.
9
0
4
left parenthesis, negative 1.0 2 , negative 1.6 2 8 , right parenthesis
−
1
.
0
2
,
−
1
.
6
2
8
left parenthesis, 0.7 9 7 9 , 0.0 1 6 2 5 , right parenthesis
0
.
7
9
7
9
,
0
.
0
1
6
2
5
left parenthesis, negative 1.7 3 3 , negative 2.2 9 , right parenthesis
−
1
.
7
3
3
,
−
2
.
2
9
left parenthesis, 1.5 0 6 , 0.0 9 5 9 8 , right parenthesis
1
.
5
0
6
,
0
.
0
9
5
9
8
left parenthesis, 0.3 1 9 5 , negative 1.7 8 5 , right parenthesis
0
.
3
1
9
5
,
−
1
.
7
8
5
left parenthesis, 1.0 2 5 , negative 0.1 5 9 9 , right parenthesis
1
.
0
2
5
,
−
0
.
1
5
9
9
left parenthesis, negative 3.0 1 3 , negative 1.9 1 1 , right parenthesis
−
3
.
0
1
3
,
−
1
.
9
1
1
left parenthesis, negative 0.2 3 6 2 , negative 0.0 7 1 , right parenthesis
−
0
.
2
3
6
2
,
−
0
.
0
7
1
left parenthesis, negative 5.5 8 9 , 4.6 7 9 , right parenthesis
−
5
.
5
8
9
,
4
.
6
7
9
left parenthesis, negative 2.6 4 , negative 0.0 5 9 7 2 , right parenthesis
−
2
.
6
4
,
−
0
.
0
5
9
7
2
left parenthesis, 2.0 1 , negative 2.6 4 6 , right parenthesis
2
.
0
1
,
−
2
.
6
4
6
left parenthesis, negative 0.2 8 9 7 , negative 1.0 6 4 , right parenthesis
−
0
.
2
8
9
7
,
−
1
.
0
6
4
left parenthesis, negative 2.9 3 5 , negative 2.8 6 4 , right parenthesis
−
2
.
9
3
5
,
−
2
.
8
6
4
63 element list
23
Hidden Label: "P" Subscript, "r" "o" "j" , Baseline left parenthesis, "c" Subscript, "e" "n" "t" "e" "r" , Baseline for "i" equals left bracket, 1...1 0 , right bracket , right parenthesis
P
r
o
j
c
e
n
t
e
r
f
o
r
i
=
1
.
.
.
1
0
Label
equals
=
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
left parenthesis, 0 , 0 , right parenthesis
0
,
0
24
Expression 25: "c" Subscript, "e" "n" "t" "e" "r" , Baseline equals left parenthesis, 0 , 3 , 0 , right parenthesis
c
e
n
t
e
r
=
0
,
3
,
0
25
Expression 26: alpha equals 1.0 7 1
α
=
1
.
0
7
1
0
0
2 pi
2
π
26
Expression 27: phi equals StartFraction, pi Over 6 , EndFraction
ϕ
=
π
6
equals
=
0.5 2 3 5 9 8 7 7 5 5 9 8
0
.
5
2
3
5
9
8
7
7
5
5
9
8
27
Hidden Label: left parenthesis, 2 alpha , 2 phi , right parenthesis
2
α
,
2
ϕ
Label
equals
=
left parenthesis, 2.0 9 7 4 , 1.0 4 7 1 9 7 5 5 , right parenthesis
2
.
0
9
7
4
,
1
.
0
4
7
1
9
7
5
5
28
Expression 29: beta equals 3.4 1 3
β
=
3
.
4
1
3
0
0
2 pi
2
π
29
Expression 30: "w" Subscript, "h" "i" "t" "e" , Baseline equals hsv left parenthesis, 0 , 0 , 1 , right parenthesis
w
h
i
t
e
=
h
s
v
0
,
0
,
1
30
31
powered by
powered by
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
Log In
or
Sign Up
to save your graphs!
New Blank Graph
Examples
Lines: Slope Intercept Form
example
Lines: Point Slope Form
example
Lines: Two Point Form
example
Parabolas: Standard Form
example
Parabolas: Vertex Form
example
Parabolas: Standard Form + Tangent
example
Trigonometry: Period and Amplitude
example
Trigonometry: Phase
example
Trigonometry: Wave Interference
example
Trigonometry: Unit Circle
example
Conic Sections: Circle
example
Conic Sections: Parabola and Focus
example
Conic Sections: Ellipse with Foci
example
Conic Sections: Hyperbola
example
Polar: Rose
example
Polar: Logarithmic Spiral
example
Polar: Limacon
example
Polar: Conic Sections
example
Parametric: Introduction
example
Parametric: Cycloid
example
Transformations: Translating a Function
example
Transformations: Scaling a Function
example
Transformations: Inverse of a Function
example
Statistics: Linear Regression
example
Statistics: Anscombe's Quartet
example
Statistics: 4th Order Polynomial
example
Lists: Family of sin Curves
example
Lists: Curve Stitching
example
Lists: Plotting a List of Points
example
Calculus: Derivatives
example
Calculus: Secant Line
example
Calculus: Tangent Line
example
Calculus: Taylor Expansion of sin(x)
example
Calculus: Integrals
example
Calculus: Integral with adjustable bounds
example
Calculus: Fundamental Theorem of Calculus
example
Terms of Service
|
Privacy Policy
