0 times anything is 0. so 0 * (x - 5) * (x-3) is still 0.
that is why when you solve equation (x-5)(x+3) = 0, you can conclude you can have either x = 5 or x = -3 to satisfy. so yes x = 5 and x = -3 are the zeros
if you know that you have a quadratic with two zeros, the vertex is in between them. it is symmetric.
so the middle of 5 and -3 is (5+ -3)/2 = 2/2 = 1.
so 1 is the x-coordinate of vertex. it is at axis of symmetry. so if you plug 1 into the function, you get y-coordinate of
y = (1-5)(1+3) = (-4)(4) = -16
so the vertex is (1,-16)
