Finding the intercept form from graph and zeros (x values)

Question

I don't know how to find the intercept form if you are given just the graph and the zeros (x values). I know that it is quadratic and not linear if that helps. I can't insert a picture because it is on paper, but I need help understanding how to do this.

Answer 1

the zeros are the x intercepts = where the graph crosses the x axis

call them b and c

then the equation is y=a(x-b)(x-c)

expand to get

y =a(x^2-(b+c)x +bc)

y = ax^2 -a(b+c)x + abc

where abc = the y intercept = where the graph crosses the y axis

(this ignores where the graph never touches the x axis, as then the zeros are imaginary. Or when the graph doesn't cross but just touches the x axis, then there is just one zero, but it repeats, or has multiplicity 2)