Quadratic Function
The derivative of the given quadratic is (dy)/(dx) = 2x 4 By observation, this is equal to 0 when x=2 When x=2 the original equation becomes y = (2)^2 4(2)12 y = 16 Therefore the vertex of this parabola is at (2,16)Consider the length of chord passing through the vertex and inclined to the xaxis at an angle θ is L then the coordinate of point where chord cut the parabola is (x 1, y 1) = (Lcos θ, Lsin θ) This point is satisfying the equation of parabola y 2 = x ⇒ (Lsin θ) 2 = Lcos θ ⇒L 2 sin 2 θ = Lcos θ