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Quadratic Equation Solver
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Standard Deviation
Standard Deviation
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16
Roots
Roots
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18
Old Quadratic Formula
Old Quadratic Formula
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21
Legend Parameters
Legend Parameters
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24
Green Stuff
Green Stuff
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34
Formulas
Formulas
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48
Solutions
Solutions
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57
Derivation
Derivation
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"f" ( "x" ) equals ( 2 ) "x" squared plus ( negative 20 ) "x" plus ( 37.5 )
f
(
x
)
=
(
2
)
x
2
+
(
−
2
0
)
x
+
(
3
7
.
5
)
"m"
m
"r" Subscript, 1 , Baseline
r
1
"r" Subscript, 2 , Baseline
r
2
"d"
d
"d"
d
Old Quadratic Formula
"x" equals StartFraction, negative "b" plus-or-minus StartRoot, "b" squared minus 4 "a" "c" , EndRoot Over 2 "a" , EndFraction
x
=
−
b
±
b
2
−
4
a
c
2
a
New Quadratic Formula
"x" equals "m" plus-or-minus StartRoot, "m" squared minus "p" , EndRoot
x
=
m
±
m
2
−
p
where
"m" equals StartFraction, negative "b" prime Over 2 , EndFraction
m
=
−
b
′
2
"p" equals "c" prime
p
=
c
′
Solutions
"x" equals "m" plus-or-minus "d"
x
=
m
±
d
"m" equals 5
m
=
5
"d" equals 2.5
d
=
2
.
5
"x" equals 5 plus-or-minus 2.5
x
=
5
±
2
.
5
"r" Subscript, 1 , Baseline equals 2.5
r
1
=
2
.
5
"r" Subscript, 2 , Baseline equals 7.5
r
2
=
7
.
5
"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
+
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