2. Graphs of x 3 (cubic graphs)
In mathematics, a cubic graph is defined as a graph
with it’s representing equation having it’s degree or
it’s highest power three with the general form:
y = ax3 + bx2 + cx + d
Where a, b and c are the co-efficents of x3, x2 and x
respectively and d is the y-intercept.
Now we would explore the effect of each of the
variable on the graph formation in detail.
3. This is a simple Graph of x3 where it’s coefficient is 1 and no other
terms are present, including the y-intercept ‘d’. Therefore, this
line passes through the origin.
Effect of the
co-efficient of X3
4. However If we further increase the coefficient of x3,we would
notice that the graph gets closer to the y-axis. The larger the
value of a, the closer the graph will be to the y-axis
5. On the other hand, if we invert the sign of the x3 co-efficient i.e.
make it negative, the graph will rise from right to left instead of
rising from left to right as illustrated below:
6. If an x2 variable is added in the equation, it would initially have no
effect on the graph formation.
Effect of the
co-efficient of X2
7. But if we keep on increasing it’s value, we would see that a wave would
start to form in the graph, which would keep on increasing in height. The
graph would form in an increasing-decreasing-increasing manner.
8. On inverting the sign of the x2 co-efficient, we see that the
wavelength remains same, but the wave of the graph is formed
below the x-axis.
9. To the same equation, if we add an x variable, the amplitude
(height) of the graph will decrease
Effect of x and it’s
co-efficient
10. If we keep on increasing it’s magnitude, the amplitude of the wave
will keep on decreasing until it becomes 0;
11. If we further increase it, the the curve will start to become
straight until it almost becomes a straight line. Later, It would
become parallel to the y-axis.
NOTE:
This Would
become parallel
to the y-axis later.
12. On the other hand, if we decrease the x co-efficient, the
amplitude of the wave will continue to increase:
13. Now the last variable in the General equation is ‘d’, which is the
y-intercept. Without d, the graph would pass through the origin as we had
observed in the first example. On it’s inclusion, the graph would cut the y-axis
according to it’s value.
Significance of the
Y-intercept
14. F O R V I E W I N G T H I S P R E S E N T A T I O N
JAZAKALLAH
