Što je oblik vrha y = 1 / 5x ^ 2 + 7 / 13x-2?

Odgovor:

#y = (1/5) (x + 35/36) ^ 2 - 1597/676 #

Obrazloženje:

#y = (x ^ 2) / 5 + (7x) / 13 - 2 #

x-koordinata vrha:

#x = -b / (2a) = ((-7) / 13) (5/2) = - 35/26 #

y-koordinata vrha:

#y (-35/26) = (1/5) (1225) / 676) - (7/13) (35/26) - 2 = #

= 245/676 - 245/338 - 2 = - 245/676 - 1352/676 =

= - 1597/676

Faktorski oblik y:

#y = a (x + b / (2a)) ^ 2 + y (-b / (2a)) #

#y = (1/5) (x + 35/26) ^ 2 - 1597/676 #