your table of value would probably look like this:
when you draw the graph manually, you plot the points from the table of values and then sketch the graph by connecting the points.
when the table of values changes from positive to negative, that means the graph is crossing the x-axis somewhere in between.
for example:
when x = -4, the graph is positive.
when x = -3, the graph is 0.
when x = -2, the graph i negative.
the graph is crossing the x-axis between x = -4 and x = -2.
you create the table by analyzing the value of p(x) = y at different values of x.
for example, at x = 1, P(x) = y = x^4 - x^3 - 13x^2 + x + 12 becomes 1^4 - 1^3 - 13 * 1^2 + 1 + 12 which becomes 1 - 1 - 13 + 1 + 12 = 0.
this can be seen both on the graph and the table of values.
the coordinate points on the graph are in (x,y) format.
for example, (1,0) means the value of x is 1 and the corresponding value of y is 0 when the value of x is equal to 1.
let me know if you have any questions.
theo
