AS/A2
Pure 1
Pure 3
P2
Topic 2:
Functions
A cubic curve
The graph shown is y=ax
3
+bx
2
+cx+d. Investigate the effect of changing
e
,
f
,
g
or
h
and decide which of these is a, b, c and d.
Summary
e = b, f = c, g = d, h = a
When
a
=0 the curve is quadratic
When
a
=0 and b=0 the curve is linear
When
a
>0 the cubic curve ranges from bottom left to top right
When
a
<0 the cubic curve ranges from top left to bottom right
The value of
d
determines the y-intercept
When
a
is non-zero, the curve may cross the x-axis at 1, 2 or 3 places
Based on free Java applets from
JavaMath
Based on
free Java applets from