graph f(x)=-x^4+3x^2+x-2 by making a table of values. Then determone the values of x between which the real zeros are located.

Question

Honors Algebra II with Trig

Answer 1

By applying the rational root theorem, the only possible roots are -2, -1, 1, and 2.  These will be the x values to use in our table for reference.

 

The table is as follows:

 

x      |       f(x)

___________

 

-3

-2

-1

0

1

2

3

 

 

Evaluate f(x) by plugging in the corresponding x values.  Record the f(x) values in the table.  Once you have done that, use the value f(x) values from the table to determine which values of x have zeros.  If consecutive f(x) values changes signs, then the zeros lie between the x values that give those f(x) values.

 

For example:

 

If f(1) was negative and f(3) was positive, then the zeroes would lie between x=1 and x=3.  This is what we call the intermediate value theorem.  This theorem can only be applied when you have a continuous function, that is a linear or polynomial function.

 

Then to draw the graph, plot the points based on the table and connect them.  You can also get your zeros from the graph.  The zeros occur where the graph crosses the x-axis.