a) Since the graph cuts the y-axis at (4,0) ,sub y = 0 , x = 4 to y = (x-3)^2 + k ,0 = (4-3)^2 + kk = - 1
i.e.
y = (x-3)^2 - 1sub x = 0 to the equation , y = (0-3)^2 - 1 = 8A is (0 , 8)
b)y = (x-3)^2 - 1When x = 3 , the minium value of y = - 1 ,So C is (3 , - 1)The area of △AOC = (1/2) * AO * height= (1/2) * 8 * 3= 12