HallsofIvy said:The graph is of y= x^2+ ax+ b and we are told that the graph goes through (2, 0). That means that when x= 2, y= 0. So we must have 0= 2^2+ a(2)+ b= 4+ 2a+ b or 2a+ b= -4. We are also told that the graph goes through (4, 0). That means that when x= 4, y= 0. So we must have 0= 4^2+ a(4)+ b= 16+ 4a+ b or 4a+ b= -16.
Solve the two equations, 2a+ b= -4 and 4a+ b= -16, for a and b.