Math Help PLEASE! Functions?

Question

can somebody explain how I answer write this question? I know what the zeroes are im just not sure about the last two points...

Determine the equation if the zeroes are -2 and 3 and the graph passes through the point (1,4)

Determine the equation if the zeroes are -3, 1 and 2 and the y-intercept is 3

I dont mean to sound retarded, but can anyone walk me through this step by step? It doesnt have to be in factored form, i just need to know the equation, stating the zeroes

Answer 1

so factors are (x+2) and (x-3)
making the equation be y = k(x^2 - x - 6)

When x=1 y = 4 so put 1 for x and 4 for y:
4 = k(1 - 1 - 6)
4 = -6k
k = 4/-6 = -2/3

Answer 2

If the zeroes are -2 and 3, the equation is of the form

y = c(x - (-2))(x - 3)

or more simply,

y = c(x+2)(x-3)

for some number c which you are to determine. To do this, note that the point (1,4) must satisfy the equation, so set x=1 and y=4 in the equation and solve for c.

The second question is very similar. What point (x,y) is indicated by "the y-intercept is 3"?