Question

Find a parabola, passing through the origin, whose tangent line at (2, 8) passes through the point (0, 16).

Answer 1

find the slope of the tangent line which is (16-8)/(0-2)=-4
plug in to a linear equation to get 8=-4(2)+b. b=16
integrate y=-4x+16 to get y=-2x^2+16x+c
plug in (0,0) to find that c=0
y=-2x^2+16x

Answer 2

it's telling me it's wrong :(