For f(x) = a*(x + b)^2 - 8 to have a tangent y = 2x at (4,8) two conditions have to be met:
1. f(4) = 8 [the parabola passes through (4,8)]
2. f'(4) = 2 [the tangent of the parabola at (4,8) is 2]
To satisfy condition 1,
a*(4 + b)^2 - 8 = 8
a*(4 + b)^2 = 16 -- eq.1
To satisfy...