Caroline is correct because the equation y = (x-1)(x-5) is in factored form. If you solve the terms (x-1) and (x-5), you get the zeros (aka x-intercepts) of the graph.
Solve (set the terms equal to 0):
x-1 = 0 x = 1
x-5 = 0 x = 5
∴ the x-intercepts are (1,0) and (5,0).
The purple graph corresponds to the zeros in the equation, not the green graph. The green graph has negative x-intercepts, whereas the purple graph has positive x-intercepts like in the equation.
