C. y = - (x + 1)(x - 3)
Standard form of a parabola: y = a(x – h)^2 + k.
Since the parabola opens downwards, the leading coefficient, a, will be negative. This means option B can be ruled out as incorrect.
The vertex is at (1,4) and is also the maximum. As this is (h,k) in vertex form, you can start substituting values to find the equation. Start with y = -(x – 1)^2 + 4 and simplify by squaring the terms in parentheses and distributing the negative in front of the parentheses.
y = - (x-1)(x-1) + 4
= -(x^2 - x - x + 1) + 4
y = -x^2 + 2x + 3.
Also written as y = -(x + 1)(x - 3)
The graphed function is shown to cross the x-axis at -1 and 3.
I hope this helps a little!