y = a(x-1)^2 - a + c - 1,vertex is (1,-a+c-1)
when x = 1,y = -8/3 x + 8 = 8 - 8/3 = 16/3
therefore -a+c-1 = 16/3
when x = 0,y = c-1 = 4
therefore c = 5
a = 4 - 16/3 = -4/3
1.y = -4/3 (x-1)^2 + 16/3
2.B (-1,0),C(3,0)
BD slope = 4
let H(x,0),K's coordinate is x+dx,y
then y = 4dx
triangle's area HKC = (3-x)4dx /2 = 2(3-x)dx = 16/5 => dx = 8/[5(3-x)]
4dx = -4/3(x+dx-1)^2 + 16/3
32 /(5(3-x)) + 4/3(x + 8/(5(3-x))-1)^2 - 16/3 = 0
solve for x and then get equation
H' coordinate is (1.23,0)
3.