vertex form of a parabola is:
y = a(x - h)^2 + k
Where vertex (h,k) is given to be (1,0) and x terms are factorable by "a" = -3
y = -3(x-1)^2 + 0
expand the parenthesis
y = -3(x-1)(x-1)
y = -3(x^2 - x - x + 1)
multiply -3 through parenthesis
y = -3x^2 + 6x - 3
Compare to given equation
c = -3