Graphing Polynomial Functions

Sketch the graph of y = 2(x + 1)(x - 1)(x - 2):

  1. Find the zeros by setting each factor equal to 0.


    2. x + 1 = 0      x - 1 = 0        x - 2 = 0
          x = -1           x = 1             x = 2

    Graph these values on the x-axis.
     

  2. Choose a number greater than 2 and substitute it into the equation.

    3. Say,  let  x = 3.  Then y = 2(4)(2)(1) = 16.  Graph (3,16).

    Choose a number between 1 and 2 and substitute it into the equation.
    Say,  let  x = 1.5.  Then y = 2(2.5)(.5)(-.5) = -1.25.  Graph (1.5,-1.25).

    Choose a number between -1 and 1 and substitute it into the equation.
    Say,  let  x = 0.  Then y = 2(1)(-1)(-2) = 4.  Graph (0,4).

    Choose a number less than -1 and substitute it into the equation.
    Say,  let  x = -2.  Then y = 2(-1)(-3)(-4) = -24.  Graph (-2,-24).
     

  3. Sketch the curve, using the above points as a guide.  This is not a perfect graph,

    4. just a sketch of the function.

Intermediate Value Theorem:


If f is a continuous function such that  f(a) ¹ f(b),  then, in the interval [a,b],
f   takes on every value between f(a) and f(b).

Problems

Go to Polynomial and Rational Functions Lesson Page
Go to Precalculus Page
Go to Precalculus Lesson Page