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IB DP Maths: AA HL复习笔记2.2.2 Factorising & Completing the Square
Category:
IB课程
,
教材笔记
,
福利干货
Date: 2022年7月11日 下午5:38
Why is factorising quadratics useful?
Factorising gives
roots (zeroes or solutions)
of a quadratic
It gives the
x
-intercepts
when drawing the graph
How do I factorise a monic quadratic of the form
x
2
+
bx
+
c
?
You might be able to spot the factors by
inspection
Especially if
c
is a
prime number
Otherwise find two numbers
m
and
n
..
A sum equal to
b
How do I factorise a non-monic quadratic of the form
ax
2
+
bx
+
c
?
If
a, b & c
have a common factor then first factorise that out to leave a quadratic with coefficients that have
no common factors
You might be able to spot the factors by
inspection
Especially if
a
and/or
c
are
prime numbers
Otherwise find two numbers
m
and
n
..
A sum equal to
b
How do I use the difference of two squares to factorise a quadratic of the form
A
2
x
2
-
C
2
?
The
difference of two squares
can be used when...
There is
no
x
term
The
constant term is a negative
Square root the two terms
A
2
x
2
&
C
2
The two factors are the
sum of square roots
and the
difference of the square roots
A shortcut is to write:
Exam Tip
Worked Example
Completing the Square
Why is completing the square for quadratics useful?
Completing the square gives the
maximum/minimum
of a quadratic function
This can be used to define the
range
of the function
It gives the
vertex
when drawing the graph
It can be used to
solve quadratic equations
It can be used to derive the
quadratic formula
How do I complete the square for a monic quadratic of the form
x
2
+
bx
+
c
?
Exam Tip
Worked Example
转载自savemyexams
Previous post: Edexcel IGCSE Biology 复习笔记 3.2.1 DNA & the Genome
Next post: Edexcel IGCSE Biology 复习笔记 3.2.2 Protein Synthesis
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