__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 trinomial inside the parenthesis is factorable by the product of two binomials? Let's factor the above equation as follows

If we set y = 0, then the x-intercepts of the given equation are 3, and -1.

If we set x = 0, then 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 < -1, then y = (-)²(-)² = (+)

If -1 < x < 0, then y = (-)²(+)² = (+)

If 0 < x < 3, then y = (-)²(+)² = (+)

If x > 3, then y = (+)²(+)² = (+)

Here's the graph of a polynomial:

Photo by Math Principles in Everyday Life |