Ano ang vertex form ng y = (5x + 2) ^ 2 + 11x (5x + 2) +30?

Sagot:

# y = 80 (x ^ 2 + 21/80) ^ 2 + 2279/80 #

Paliwanag:

Una naming pasimplehin ito.

# y = (5x + 2) ^ 2 + 11x (5x + 2) + 30 #

# = 25x ^ 2 + 20x + 4 + 55x ^ 2 + 22x + 30 #

# = 80x ^ 2 + 42x + 34 #

# = 80 (x ^ 2 + 42 / 80x) + 34 #

# = 80 (x ^ 2 + 2xx21 / 80x + (21/80) ^ 2- (21/80) ^ 2) + 34 #

# = 80 (x ^ 2 + 21/80) ^ 2- (21/80) ^ 2xx80 + 34 #

# = 80 (x ^ 2 + 21/80) ^ 2-441 / 80 + 34 #

# = 80 (x ^ 2 + 21/80) ^ 2 + 2279/80 #

na nasa vertex form at vertex ay #(-21/80,2279/80)# o #(-21/80,28 39/80)# at lilitaw ang graph tulad ng sumusunod:

graph {80x ^ 2 + 42x + 34 -2, 2, -10.9, 149.1}

Sagot:

# y = 80 (x ^ 2 + 21/80) ^ 2 + 2279/80 #

Paliwanag:

Una naming pasimplehin ito.

# y = (5x + 2) ^ 2 + 11x (5x + 2) + 30 #

# = 25x ^ 2 + 20x + 4 + 55x ^ 2 + 22x + 30 #

# = 80x ^ 2 + 42x + 34 #

# = 80 (x ^ 2 + 42 / 80x) + 34 #

# = 80 (x ^ 2 + 2xx21 / 80x + (21/80) ^ 2- (21/80) ^ 2) + 34 #

# = 80 (x ^ 2 + 21/80) ^ 2- (21/80) ^ 2xx80 + 34 #

# = 80 (x ^ 2 + 21/80) ^ 2-441 / 80 + 34 #

# = 80 (x ^ 2 + 21/80) ^ 2 + 2279/80 #

na nasa vertex form at vertex ay #(-21/80,2279/80)# o #(-21/80,28 39/80)# at lilitaw ang graph tulad ng sumusunod:

graph {80x ^ 2 + 42x + 34 -2, 2, -10.9, 149.1}