how do i find a possible equation for a graph with points (3,0) (1,0) (2,-1) (0,3)

Question

x-axis = -1 thru 3

y-axis = -2 thru 3

Answer 1

A sketch of the graph shows that the curve cuts the y-axis at y=3; then it meets the x axis at x=1, dips below it so that at x=2 y=-1, then it turns round to cut the x axis again at x=3. It looks like a parabola with vertex at (2,-1). We know when x=1 and 3, y=0, so it would appear that the equation is y=(x-1)(x-3). All we have to do now is check it out. We know the roots are correct. When x=0, y does equal 3; when x=2, y=-1, so that fits the point (0,3) and (2,-1). So the equation is indeed y=(x-1)(x-3) or x^2-4x+3.