I have been pondering this question for a little while, and unfortunately the Google has not given me an answer.
I understand that for example you had a table or graph that crosses or touches the x axis at say x= -2, 0, 3 you could form an equation as
f(x) = ax(x+2)(x-3)
Then solve for a and you have your function.
I have considered transforming a graph to force zeros, and in the couple of attempts I made, it was successful, but I am unsure if this would be the mathmatically proper way to do so.
So my question is if you have a graph or table of coordinates similar to my example above, but the points never cross zerI, what would be the proper Mathmatics procedure to find the equation.
y = x^2. Vertex = 0,0 and zero = 0
In comparison to:
y = (x-1)^2+1 vertex = 1,1 and zero = null
Its the same form but in a different position. In this situation the functions were provided, but for clarification of what I am looking for, I thought this would help.