Graphs of x3 function

I have covered the effect on the graph of a, x3, b, x2, c, x and d from the general equation ax3+bx2+cx+d

1. EXPLORING CUBIC GRAPHS ABDUL MOIZ STUDENT AT GENERATIONS SCHOOL- O LEVELs

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 = ax 3  + bx 2  + cx + d Where a, b and c are the co-efficents of x 3 , x 2 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 x 3 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 X 3

4. However If we further increase the coefficient of x 3 , 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 x 3 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 x 2 variable is added in the equation, it would initially have no effect on the graph formation. Effect of the co-efficient of X 2

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 x 2 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