form 4 math function and graph

(a) Sub the points (0,-3) and (1,0) into equation
-3 = b - (0 + a)^2
-3 = b - a^2 ... (1)
0 = b - (1 + a)^2
0 = b - 1 - 2a - a^2 ... (2)
(2) - (1) => 3 = -1 - 2a
=> a = -2
Sub into (1), -3 = b - 4 => b = 1
0 = b - (c + a)^2
0 = 1 - (c - 2)^2
(c - 2)^2 = 1
c - 2 = +/- 1
c = 1 (rejected) or c = 3
(b) y = 1 - (x - 2)^2
The greatest value of y is 1 when x = 2
(c) the axis of symmetry is x = 2