60 points & Brainliest! (Please show all steps)

g(x) = (x + 2)(x - 1)(x - 2)

a1) Find the zeros of the function.
a2) Show How you found the Zeros

b1) Find the y-intercept of the function.
b2) Show your work

c) Create the graph of the polynomial.
D) Describe the end behavior of the graph.

See below .

Step-by-step explanation:

This is a cubic function whose graph will contain 2 loops.

a)  (x + 2)(x - 1)(x - 2) = 0

Since this a product of 3 terms and the result is zero all 3 could be  zero so we have:

x + 2 = 0, x - 1 = 0 or x - 2 = 0

So the zeroes are -2, 1 and 2.

b) the y -intercept occurs when x = 0 , so substituting for x:

y-intercept =   (0 + 2)(0 - 1)(0 - 2) = 2*-1*-2 =  4 = y coordinate of the y-intercept

y-intercept  is at (0, 4).

c)  Plot the points  (-2, 0), ( 1, 0), ( 2, 0) and (0, 4).

Also I suggest you  you plot  some points (-1, 6) and  (1.5 , -0.9) where the graph will  have loops.

d) As the leading coefficient  is positive  the graph will fall to the left and rise to the right.