Aká je os symetrie a vrcholu pre graf y = -3x ^ 2 + 12x + 4?

odpoveď:

aos = 2

vrchol = (2,16)

#y = -3x ^ 2 + 12x + 4 #

#f (x) = -3x ^ 2 + 12x + 4 #

Vo forme # Y = ax ^ 2 + bx + c # máš:

# A = -3 #

# B = 12 #

# C = 4 #

Os symetrie (aos) je: #aos = (- b) / (2a) = (-12) / (2 * -3) = 2 #

pamätať # Y = f (x) #

Vertex je: # (aos, f (aos)) = (2, f (2)) #:

#f (x) = -3x ^ 2 + 12x + 4 #

#f (2) = -3 (2) ^ 2 + 12 * 2 + 4 = 16 #

vrchol #=(2, 16)#

graf {-3x ^ 2 + 12x + 4 -16,71, 23,29, -1,6, 18,4}

Vertex -

#(2,16)#

Os symetrie

# X = 2 #

Vzhľadom na -

# Y = -3x ^ 2 + 12x + 4 #

Vertex -

#X = (- b) / (2a) = (- 12) / (2xx-3) = (- 12) / (- 6) = 2 #

na # X = 2; y = 3 (2 ^ 2) 12 (2) + 4 #

# Y = -12 + 24 + 4 = 16 #

#(2,16)#

Os symetrie

# X = 2 #