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IB DP Maths: AA HL复习笔记2.2.4 Quadratic Inequalities
Category:
IB课程
,
教材笔记
,
福利干货
Date: 2022年7月11日 下午5:55
What affects the inequality sign when rearranging a quadratic inequality?
The inequality sign is
unchanged
by...
Adding/subtracting
a term to both sides
Multiplying/dividing
both sides by a
positive term
The inequality sign
flips
(< changes to >) when...
Multiplying/dividing
both sides by a
negative term
How do I solve a quadratic inequality?
STEP 1
:
Rearrange
the inequality into quadratic form with a
positive squared term
ax
2
+
bx
+
c > 0
ax
2
+
bx
+
c ≥ 0
ax
2
+
bx
+
c < 0
ax
2
+
bx
+
c ≤ 0
STEP 2
: Find the
roots
of the quadratic equation
Solve
ax
2
+
bx
+
c
= 0 to get
x
1
and
x
2
where
x
1
<
x
2
STEP 3
:
Sketch
a graph of the quadratic and label the roots
As the squared term is positive it will be
concave up
so "U" shaped
STEP 4
:
Identify
the
region
that satisfies the inequality
If you want the graph to be
above the
x
-axis
then choose the region to be the
two intervals outside
of the two roots
If you want the graph to be
below the
x
-axis
then choose the region to be the
interval between
the two roots
For
ax
2
+
bx
+
c > 0
The solution is
x
<
x
1
or
x
>
x
2
For
ax
2
+
bx
+
c ≥ 0
The solution is
x
≤
x
1
or
x
≥
x
2
For
ax
2
+
bx
+
c < 0
The solution is
x
1
<
x
<
x
2
For
ax
2
+
bx
+
c ≤ 0
The solution is
x
1
≤
x
≤
x
2
How do I solve a quadratic inequality of the form (
x -
h)
2
<
n
or (
x -
h)
2
>
n
?
The safest way is by following the steps above
Expand and rearrange
Exam Tip
Worked Example
转载自savemyexams
Previous post: Edexcel IGCSE Biology 复习笔记 3.2.6 Variation
Next post: Edexcel IGCSE Biology 复习笔记 3.2.7 Mutation
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