Science++

Maximum and Minimum Value of Quadratic function f(x) :

Vertex of parabola :

( y+D/4a) = a (x +b/2a)^{2   ….(1)}

^{let  y + D/4a = Y & x + b/2a = X}

   ^∴             Y = aX²

Y=0                          &              X=0

^{y + D/4a=0           &             x + b/2a=0}

^{y = -D/4a                               x = -b/2a}

^{Vetex = ( -b/2a , -D/4a)}

^{Case1 : a > 0 then f(x) has minimum value at x=-b/2a}

^{f(-b/2a) = -D/4a}