__Category__: Analytic Geometry"Published in Vacaville, California, USA"

Sketch the graph of a polynomial:

__Solution__:

Consider the given equation above

Did you notice that the given equation is a perfect trinomial square? Let's factor the above equation as follows

and then it is factorable by the difference of two cubes as follows

If we set y = 0, then we can solve for the value of x at each factors which are the x-intercepts.

For , the value of x is

For , the value of x is

Since the roots of the second factor are imaginary numbers, then we cannot accept those values. Because of this, the only x-intercept is 1.

If we set x = 0, the y-intercept of the given equation is

Since we now the x-intercept, then we can sketch the location or direction of a curve as follows

If x < 0, then y = (-)²(+)² = (+)

If 0 < x < 1, then y = (-)²(+)² = (+)

If x > 1, then y = (+)²(+)² = (+)

Here's the graph of a polynomial:

Photo by Math Principles in Everyday Life |