answersLogoWhite

0


Best Answer

(1) Find the x-intercepts (by setting y=0 and solving for x).

(2) Find the y-intercepts (by setting x=0 and solving for y).

(3) OPTIONAL: Check for symmetries. If a point (x,y) is on the graph, is the point (-x,y) also on the graph (that is symmetry about the y-axis)? Is the point (-x,-y) on the graph (that is symmetry about the origin)? There are many kinds of symmetries.

(4) Check for vertical asymptotes--normally you would set the denominator ONLY equal to zero and solve for x, but this equation does not have any fractions, so don't worry about this step.

(5) Check for horizontal asymptotes--what is the limit of the equation as x approaches infinity? Negative infinity? (In this example the limit will not exist; the graph will go toward infinity as x gets bigger.)

(6) Use the first derivative test to find the maximums and minimums, as well as to determine the intervals where the graph increases and decreases.

(7) Use the second derivative test or concavity test to find points of inflection and/or concavity.

(8) Wherever the behavior of the graph is still unclear, simply plug in some test values for x and see what you get for corresonding y values.

User Avatar

Wiki User

12y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: How do you graph y equals x to the fourth plus 2x cubed plus x squared plus 8x minus 12 without a calculator?
Write your answer...
Submit
Still have questions?
magnify glass
imp