1.3 Equations And Graphs of Polynomial Functions

Okay now..you're walking down the road, and someone stops you and asks "how do you sketch a graph of a polynomial function?" Most probably you would think he's out of his mind, but try thinking of the question he asked... what are the factors you need to take into consideration when sketching a graph?
A polynomial function graph can be sketched using:

• x-intercepts
• the degree of the function
• sign of leading coefficient

Let's look at this example:

Given y = (x-1)(x+1)(x+3)

Degree	Leading Coefficient	End Behaviour	Zeros and x-intercept	y-intercepts
Each factor has one x. Their product is x³. The function is cubic (degree 3)	The product of all the x-coefficients is 1.	A cubic with a positive leading coefficient extends from Quadrant 1 to Quadrant 3.	The zeros are 1,-1 and -3. These are the x-intercepts.	The y-intercept is (0-1)(0+1)(0+3) = -3

  

Mark the intercepts. Since the order of each zero is 1, the graph changes sign at each x-intercepts. Beginning in quadrant 3, sketch the graph so that it passes up through x=-3 to the positive side of the x-axis, back down, through x=-1 to the negative side of the x-axis, through the y-intercept at y=-3, up through x=1, and upward in quadrant 1.

AND...that's how you sketch a graph!=D easy as ABC,isnt it? he