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Mathematics IGCSE O Level. Parabolas

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www.mathletics.com
Curriculum ReadyParabolas
Parabolas
SERIES TOPIC
K
1
100% Parabolas
Mathletics 100% © 3P Learning
Parabolas
8
How many
x
-intercepts does a quadrac equaon have?What is the turning point of a parabola?When is a turning point a maximum or minimum?
PARABOLAS
Answer these quesons,
before
working through the chapter.Answer these quesons,
after
working through the chapter.
Quadrac equaons have highest power
2
(squared). The standard form of a quadrac equaon is
y ax bx c
2
= + +
But now I think:
What do I know now that I didn’t know before?
I used to think:
How many
x
-intercepts does a quadrac equaon have?What is the turning point of a parabola?When is a turning point a maximum or minimum?
SERIES TOPIC
K 8
2
100% Parabolas
Mathletics 100% © 3P Learning
Parabolas
Basics
What is a Parabola?
A 'quadrac' equaon has the form Where
a
,
b
and
c
are constants and
0
a
!
. In other words, the highest power in a quadrac equaon is
2
(squared).
y ax bx c
2
= + +
This is called standard form
Write these quadrac equaons in standard form and nd the values of
a
,
b
and
c
a
b
c
3 4
y x x
2
= - +
3 4
y x x
2
`
=- + +
, ,
1 3 4
a b c
`
=- = =
, ,
1
a b c
0 5
`
= = =-
, ,
3 6 45
a b c
`
= =- =-
a aab bc cc
5
y x
2
= -
( )
y x x y x x y x x
3 5 33 2 153 6 45
22
``
= - += - -= - -
^ ^h h
Drawing a Parabola from a Table
The table method has been used here to draw the graph of
2
y x x
2
= - -
x
-3-2-101234
y
1040-2-20410
Each parabola has these key points:
ã Two
x
-intercepts ã A
y
-intercept ã A turning point (or 'vertex')
y x
-6 -5 -4 -3 -2 -1 1 2 3 4 5 610
9876
54321-1-2-3-40
x
-intercept
x
-intercept
y
-interceptTurning point
The graph of a quadrac equaon is called a 'parabola'.

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