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How do you write the quadratic function
y
=
−
2
x
2
+
6
x
−
3
in vertex form?
Algebra Vertex Form of a Quadratic Equation
2 Answers
Douglas K.
Oct 22, 2017
The vertex form of a quadratic of the form
y
=
a
x
2
+
b
x
+
c
is:
y
=
a
(
x
−
h
)
2
+
k
[1]
where
h
=
−
b
2
a
and
k
=
a
h
2
+
b
h
+
c
Explanation:
Given:
y
=
−
2
x
2
+
6
x
−
3
Please observe that
a
=
−
2
,
b
=
6
and
c
=
−
3
Substitute the value of
a
=
−
2
into equation [1]:
y
=
−
2
(
x
−
h
)
2
+
k
[2]
Compute the value of h:
h
=
−
6
2
(
−
2
)
h
=
3
2
Substitute the value of
h
=
3
2
into equation [2]:
y
=
−
2
(
x
−
3
2
)
2
+
k
[3]
Compute the value of k:
k
=
−
2
(
3
2
)
2
+
6
(
3
2
)
−
3
k
=
3
2
Substitute the value of
k
=
3
2
into equation [3]:
y
=
−
2
(
x
−
3
2
)
2
+
3
2
←
this is the vertex form
Answer link
sankarankalyanam
Oct 22, 2017
y
=
(
−
2
)
(
(
x
−
(
3
2
)
2
)
+
(
3
2
)
Explanation:
Vertex form of quadratic equation
a
x
2
+
b
x
+
c
is
y
=
a
(
x
−
x
s
)
2
+
y
s
x
s
=
−
b
2
a
y
s
=
−
(
b
2
4
a
)
+
c
Given equation is
y
=
−
2
x
2
+
6
x
−
3
a
=
−
2
,
b
=
6
,
c
=
−
3
x
s
=
−
6
2
⋅
(
−
2
)
=
3
2
y
s
=
−
b
2
4
a
+
c
=
−
−
6
2
4
⋅
−
2
+
(
−
3
)
=
−
(
−
9
2
)
−
3
=
3
2
y
=
−
2
⋅
(
x
−
(
3
2
)
)
2
+
(
3
2
)
Answer link
Related topic
Vertex Form of a Quadratic Equation
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