Represent the function f(x)=✓2x² - 5x +3 as a composition of two functions.
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The standard form of the
quadratic function
is.
y
=
a
x
2
+
b
x
+
c
To factorise the function.
• consider the factors of the product ac which sum to give b
for
2
x
2
+
5
x
−
3
a
=
2
,
b
=
5
and
c
=
−
3
⇒
a
c
=
2
×
−
3
=
−
6
the required factors of -6 are
+
6
and
−
1
since
6
×
−
1
=
−
6
and
+
6
−
1
=
+
5
now express
2
x
2
+
5
x
−
3
as
2
x
2
+
6
x
−
x
−
3
Factorise by 'grouping'
⇒
2
x
(
x
+
3
)
−
1
(
x
+
3
)
Take out
common factor
of
(
x
+
3
)
⇒
(
x
+
3
)
(
2
x
−
1
)
←
in factorised form
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