Graphing a Polynomial Function

Step #!:

Find the Intercepts

X intercept x1 =3, x2= -2, x3= -4 ( use the opposite numbers to determine the x intercepts) meaning it would be (3,0), (-2,0), and (-4,0)

Y intercept y = 30 ( done by doing 3x2x4=24) (by multiplying the y intercepts by the exponents and then multiplying them all together to get the y\intercept)

Step #2:

Find The Zeros

The zeros are basically when the lines cross the x access x1 = 3, x2 = -2, x3 = -4

Step #3:

Find The Degree

Add up the exponents (powers) 1 + 1 + 1 =3 meaning the polynomial function is in 3rd degree polynomial. Having a leading term of x3, and a leading coefficient of 1.

Step #4:

Find The Leading Coefficient

It is positive because the leading coefficient sign at the start of the equation is positive.

Step #5:

Find The End Behaviour

Look back at the degree found, it has a positive leading coefficient and it has an odd number ( meaning up to the right and down left ) and has a behaviour that looks like this

x →- ∞, f(x) → - ∞

x →∞, f(x) → ∞

Step #6:

Find The Order Of The x-intercept

(x-3), (x+2), and (x+4)

Creating an order of 3

Step #7:

Find The Maximum and Minimum Values

The maximum value would be approximately (-3.2)

The minimum value would be approximately (1,-6)

Step #8:

Labeling and Connecting the points

f(x) = (x-3)(x+2)(x+4)