Maximum & Minimum Value

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

maximum value

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Case2:  a > 0 then f(x) has maximum value at x=-b/2a

f(-b/2a) = -D/4a

minimum value