what is the axis of symmetry for f(x)= x2+4x+6
Answers
Step-by-step explanation:
factorise by the method of middile term factorisation.
and by u can determine the axis.
Step-by-step explanation:
Set the polynomial equal to
y
to
the properties of the
parabola.
y
=
−
2
x
2
+
4
x
−
6
Enter a problem...
Algebra Examples
Popular Problems Algebra Find the Axis of Symmetry f(x)=-2x^2+4x-6
f
(
x
)
=
−
2
x
2
+
4
x
−
6
Set the polynomial equal to
y
to find the properties of the parabola.
y
=
−
2
x
2
+
4
x
−
6
Rewrite the equation in vertex form.
Tap for fewer steps...
Complete the square for
−
2
x
2
+
4
x
−
6
.
Tap for fewer steps...
Use the form
a
x
2
+
b
x
+
c
, to find the values of
a
,
b
, and
c
.
a
=
−
2
,
b
=
4
,
c
=
−
6
Consider the vertex form of a parabola.
a
(
x
+
d
)
2
+
e
Substitute the values of
a
and
b
into the formula
d
=
b
2
a
.
d
=
4
2
(
−
2
)
Simplify the right side.
Tap for more steps...
d
=
−
1
Find the value of
e
using the formula
e
=
c
−
b
2
4
a
.
Tap for more steps...
e
=
−
4
Substitute the values of
a
,
d
, and
e
into the vertex form
a
(
x
+
d
)
2
+
e
.
−
2
(
x
−
1
)
2
−
4
Set
y
equal to the new right side.
y
=
−
2
(
x
−
1
)
2
−
4
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
−
2
h
=
1
k
=
−
4
Since the value of
a
is negative, the parabola opens down.
Opens Down
Find the vertex
(
h
,
k
)
.
(
1
,
−
4
)
Find
p
, the distance from the vertex to the focus.
Tap for more steps...
−
1
8
Find the focus.
Tap for more steps...
(
1
,
−
33
8
)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x
=
1
image of graph
([)]|√>≥
789÷<≤
456/×∩∪
123-^π∞
0.,+%=