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Quadratic function
Quadratic function
7 formulas · Mathematics
Standard form
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x)=ax^2+bx+c
f
(
x
)
=
a
x
2
+
b
x
+
c
Discriminant
Δ
=
b
2
−
4
a
c
\Delta=b^2-4ac
Δ
=
b
2
−
4
a
c
Roots (zeros)
x
1
,
2
=
−
b
±
Δ
2
a
x_{1,2}=\dfrac{-b\pm\sqrt{\Delta}}{2a}
x
1
,
2
=
2
a
−
b
±
Δ
Vertex form
f
(
x
)
=
a
(
x
−
p
)
2
+
q
f(x)=a(x-p)^2+q
f
(
x
)
=
a
(
x
−
p
)
2
+
q
Vertex coordinates
p
=
−
b
2
a
,
q
=
−
Δ
4
a
p=-\dfrac{b}{2a},\quad q=-\dfrac{\Delta}{4a}
p
=
−
2
a
b
,
q
=
−
4
a
Δ
Factored form
f
(
x
)
=
a
(
x
−
x
1
)
(
x
−
x
2
)
f(x)=a(x-x_1)(x-x_2)
f
(
x
)
=
a
(
x
−
x
1
)
(
x
−
x
2
)
Vieta's formulas
x
1
+
x
2
=
−
b
a
,
x
1
x
2
=
c
a
x_1+x_2=-\tfrac{b}{a},\quad x_1x_2=\tfrac{c}{a}
x
1
+
x
2
=
−
a
b
,
x
1
x
2
=
a
c
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