Aká je vrcholová forma y = (9x-6) (3x + 2) + 4x ^ 2 + 5x?

odpoveď:

# Y = 31 (x + 5/62) ^ 2-1513 / 124 #

vysvetlenie:

# Y = (9x-6) (3 x + 2) + 4x ^ 2 + 5x #

= # 27x ^ 2 + 18x-18x-12 + 4x ^ 2 + 5x #

= # 31x ^ 2 + 5x-12 #

= # 31 (x ^ 2 + 5 / 31x) -12 #

= # 31 (x ^ 2 + 2xx5 / 62xx x + (5/62) ^ 2- (5/62) ^ 2) -12 #

= # 31 (x + 5/62) ^ 2-31 (5/62) ^ 2 až 12 #

= # 31 (x + 5/62) ^ 2-25 / 124-12 #

alebo # y = 31 (x + 5/62) ^ 2-12 25/124 #

tj. # Y = 31 (x + 5/62) ^ 2-1513 / 124 #

a vertex je #(-5/62,-12 25/124)#

graf {y = 31 (x + 5/62) ^ 2-1513 / 124 -3, 3, -20, 20}