what is the vertex of parabola y^2+4x+2y-15=0?
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Answer:
The vertex is V = (-1,2)
The focus is F = (0,2)
The directrix is X = (-2)
Step-by-step explanation:
Let's rearrange the equation and complete the squares
y
2
−
4
y
=
4
x
y
2
−
4
y
+
4
=
4
x
+
4
(
y
−
2
)
2
=
4
(
x
+
1
)
Comparing this equation to
(
y
−
b
)
2
=
2
p
(
x
−
a
)
p
=
2
The vertex is V
=
(
a
,
b
)
=
(
−
1
,
2
)
The focus is F
=
(
a
+
p
2
,
b
)
=
(
0
,
2
)
The directrix is
x
=
a
−
p
2
x
=
−
1
−
1
=
−
2
graph{(y^2-4y-4x)(y-100x-200)=0 [-10, 10, -5, 5]}
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