GrAphs ofx3

EXPLORING CUBIC GRAPHSABDUL MOIZ STUDENT AT GENERATIONS SCHOOL- O LEVELs

Graphs of x3 (cubic graphs)In mathematics, a cubic graph is defined as a graph with its representing equation having its degree or its 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.

This is a simple Graph of x3 where its 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

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

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:

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

But if we keep on increasing its 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.

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.

To the same equation, if we add an x variable, the amplitude (height) of the graph will decrease

Effect of x and itsco-efficient

If we keep on increasing its magnitude, the amplitude of the wave will keep on decreasing until it becomes 0;

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.

On the other hand, if we decrease the x co-efficient, the amplitude of the wave will continue to increase:

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 its inclusion, the graph would cut the y-axis according to its value.

Significance of theY-intercept

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