how do you graph a polynomial function?

- Find the x-intercepts, by setting y=0 and solving the polynomial equation. You may need to factorise

- Find the y-intercepts, by setting x=0 and solving.

- Find stationary points by differentiating the polynomial equation wrt x and setting the differential to 0. These give you the stationary points.

- Differentiate again to find out whether these turning points are maxima, minima or points of inflexion:

If d²y/dx² is positive, then it is a minimum point.

If d²y/dx² is negative, then it is a maximum point

If d²y/dx² is zero, then it could be a max, a min or a point of inflexion.

- Find asymptotes. You may get a horizontal asymptote when x approaches +ve or -ve infinity and a vertical one as y approaches +ve,-ve infinity.

This is the basic info you need to sketch a graph depending on how complex the polynomial is.

Set up a desk with two columns, one for x values and one for y values. Choose the x values and calculate the y values, coming into each and every within the desk. Then plot the elements on graph paper. You might have got to use a scale component for cubic or quartics, because the values have a tendency to expand quickly. Factoring or differentiating the features, if you'll, will supply clues on what x values to decide on.

just construct a table...

let it be y=f(x)

substitute values for x say 0,1,2,3,4 and find the corresponding y values.. And then draw the graph