f.4 quadratic functions~~~

(1) The graph of y = { x - [ (a - b) / 2] }^2 + [ (a + b) / 2 ] cuts the y - axis at (0,4) and its vertex is on the x - axis. Find the values of a and b.
Vertex is [(a - b)/2, (a + b)/2] is on the x - axis
=> (a + b)/2 = 0
=> a = - b
Therefore the equation becomes y = {x - [( - b - b)/2]}^2 + ( - b + b)/2
y = (x + b)^2
Sub (0,4) to the equation, 4 = (0 + b)^2
=> b = + / - 2
when b = 2, a = - 2
when b = - 2, a = 2
(2) The graph of y = - {x - [(c - d)/2]}^2 + [(c + d)/2] cuts the x - axis at (2,0) and ( - 2,0). Find the values of c and d
Since the graph cuts the x - axis at (2,0) and ( - 2,0), y = - (x - 2)(x + 2)
y = - x^2 + 4
Therefore (c - d)/2 = 0 ... (1)
(c + d)/2 = 4 ... (2)
(1) => c = d
Sub into (2), (c + d)/2 = 4
2d/2 = 4
d = c = 4