Answer:
g(x) = (x + 2)(x − 1)(x − 2)
I picked the first one, because why not. :)
<u>End behavior.</u> 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.
<u>Y-intercept.</u> 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.
<u>Zeros / x-intercept.</u> 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).
19)
6/x = x/12
x^2 = 72
x = √72
x = 6√2
y^2 = 12^2 + (√72)^2
y^2 = 144 + 72
y^2 = 216
y = 6√6
21)
14 - 8 = 6
y/8 = 6/y
y^2 = 48
y = √48
y = 4√3
x^2 = 6^2 +(√48)^2
x^2 = 36 + 48
x^2 = 84
x = √84
x = 2√21
8 x .75 x 1.50 = 9 that is your answer