Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Equation of parabola is
4
y
=
x
2
+
4
x
+
24
Explanation:
As the vertex
(
−
2
,
5
)
and focus
(
−
2
,
6
)
share same abscissa i.e.
−
2
, parabola has axis of symmetry as
x
=
−
2
or
x
+
2
=
0
Hence, equation of parabola is of the type
(
y
−
k
)
=
a
(
x
−
h
)
2
, where
(
h
,
k
)
is vertex. Its focus then is
(
h
,
k
+
1
4
a
)
As vertex is given to be
(
−
2
,
5
)
, the equation of parabola is
y
−
5
=
a
(
x
+
2
)
2
as vertex is
(
−
2
,
5
)
and parabola passes through vertex.
and its focus is
(
−
2
,
5
+
1
4
a
)
Therefore
5
+
1
4
a
=
6
or
1
4
a
=
1
i.e.
a
=
1
4
and equation of parabola is
y
−
5
=
1
4
(
x
+
2
)
2
or
4
y
−
20
=
(
x
+
2
)
2
=
x
2
+
4
x
+
4
or
4
y
=
x
2
+
4
x
+
24
graph{4y=x^2+4x+24 [-11.91, 8.09, -0.56, 9.44]}
4
y
=
x
2
+
4
x
+
24
Explanation:
As the vertex
(
−
2
,
5
)
and focus
(
−
2
,
6
)
share same abscissa i.e.
−
2
, parabola has axis of symmetry as
x
=
−
2
or
x
+
2
=
0
Hence, equation of parabola is of the type
(
y
−
k
)
=
a
(
x
−
h
)
2
, where
(
h
,
k
)
is vertex. Its focus then is
(
h
,
k
+
1
4
a
)
As vertex is given to be
(
−
2
,
5
)
, the equation of parabola is
y
−
5
=
a
(
x
+
2
)
2
as vertex is
(
−
2
,
5
)
and parabola passes through vertex.
and its focus is
(
−
2
,
5
+
1
4
a
)
Therefore
5
+
1
4
a
=
6
or
1
4
a
=
1
i.e.
a
=
1
4
and equation of parabola is
y
−
5
=
1
4
(
x
+
2
)
2
or
4
y
−
20
=
(
x
+
2
)
2
=
x
2
+
4
x
+
4
or
4
y
=
x
2
+
4
x
+
24
graph{4y=x^2+4x+24 [-11.91, 8.09, -0.56, 9.44]}
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
