Here is the answer for my problem :

1/ We have x - intercept is only -4 , that means the vertex of this function's graph will be (-4, 0), and this x-intercept or this zero will be Double root.

As the theme, this polynomial function is a quadratic one, so it has two "square" (two zeros) or it is in form a(x - r1)(x - r2)

So, The equation will be y = a(x + 4)^2(x - r2)
We also have y-intercept is -8 , that means : The graph will be downward/the leading coefficient will be negative.

The point (0, -8) will be on the graph.

So far, we have : -8 = a(0 + 4)^2 and then solve for a, we'll get a = -2

Eventually, our equation is y = -2(x+4)^2
2/For this graph, i will do like this :

When we have a graph of any polynomial function, first, we need to identify the sign of "a", leading coefficient whether positive or negative by looking at its graph.

In the second picture, the "a" is negative.
Then, we need to realize what the degree of this function.

In this case, the degree is 5.
Set up the parenthesis based on the degree and the graph. In this case, we will have y = -()()^3()

Seek for the x-intercepts to fill out the set above. In this case, we have x-intercepts are -5, -2, 1 .

So, y = -(x+5)(x+2)^3(x-1)