2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
o g(x) = (x + 2)(x − 1)(x − 2)
o g(x) = (x + 3)(x + 2)(x − 3)
o g(x) = (x + 2)(x − 2)(x − 3)
o g(x) = (x + 5)(x + 2)(x − 5)
o g(x) = (x + 7)(x + 1)(x − 1)

g(x) = (x + 2)(x − 1)(x − 2)

I picked the first one, because why not. :)

End behavior. This is a positive function; there are no negatives next to any of the xs. There are 3 xs, so it's a cubic; a positive cubic has a down-up end behavior.

Y-intercept. We can either graph this on the calculator/online or work it out algebraically. Multiply together the constants: +2 * -1 = -2, -2 * -2 = 4. So the y-intercept is at y = 4. (0,4). I've also attached the graph.

Zeros / x-intercept. This is really simple: set g(x) equal to 0, separate these three parenthesis (x+2) (x-1) and (x-2) into three equations by the Zero Product Property.

x+2 = 0

x = -2

x-1 = 0

x = 1

x-2 = 0

x = 2

So the function has three zeros at (-2,0) (1,0) and (2,0).

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.