find the third degree polynomial whose graph is show in the figure.?

Question

the figure has this points x, y: (-2,0) ; (2,0) ; (2,0)
answer options are:
a) f(x) = x^3 -x^2-2x+2
b) f(x) = 1/4x^3 -1/2x^2-x+2
c) f(x) =1/4 x^3 -1/4x^2+2x+2
d) f(x) = 1/2x^3 -1/2x^2-x+2

Answer 1

Plugging in (2,0) rules out (a);

x^3 - x^2 - 2x + 2 =
8 - 4 - 4 + 2 =
2
(when x=2, f(x)=2, not 0)

Plugging in (2,0) rules out (c):

1/4 x^3 -1/4x^2+2x+2 =
1/4 * 8 - 1/4 * 4 + 2*2 + 2 =
2 - 1 + 4 + 2 =
7
(when x=2, f(x)=7, not 0)

Plugging in (2,0) rules out (d):

1/2x^3 -1/2x^2-x+2 =
1/2 * 8 - 1/2*4 - 2 + 2 =
4 - 2 - 2 + 2 =
2
(when x=2, f(x)=2, not 0).

That leaves only (b), which does fit:

1/4x^3 -1/2x^2-x+2 =
1/4 * 8 - 1/2 * 4 - 2 + 2 =
2 - 2 - 2 + 2 =
0
(when x=2, f(x) = 0)

Of the four equations given as possible solutions, only (b) would yield f(2)=0.

Answer 2

f(x)= a(x+one million)(x-3/2)(x-3) u understand a ingredient of the graph: (0 3.5) plug this ingredient into the equation. f(0) = 3.5 = a(0+one million)(0-3/2)(0-3) 7/2 = a(one million)(-3/2)(-3) = a(9/2) 7/2 * 2/9 = a = 7/9 a = 7/9, like ur answer says