The equation 3 = a x (1)^2 x (-3)^2 is derived by substituting x=0 into the expressions a(x+1)^2 and (x-3)^2, resulting in a(1)^2 and (-3)^2 respectively. The values x=0 and y=3 are confirmed by the graph, where the function intersects the y-axis at a y-value of 3. This substitution leads to the conclusion that the equation holds true. Additionally, -1 and 3 are identified as roots of multiplicity 2, as they are both roots of y(x)=0 and local minima of y'(x)=0. The discussion clarifies the relationship between the graph and the equation.