Hvad er vertexet for y = 2 (x / 2-2) ^ 2-4?

Hvad er vertexet for y = 2 (x / 2-2) ^ 2-4?
Anonim

Svar:

Vertex #(4, -4)#

Forklaring:

Givet -

# Y = 2 (x / 2-2) ^ 2-4 #

# Y = 2 (x ^ 2 / 4-2x +4) -4 #

# y = 1/2 x ^ 2-4x + 8-4 #

# y = 1/2 x ^ 2-4x + 4 #

Vertex -

#x = (- b) / (2a) = (- (- 4)) / (2 xx 1/2) = 4/1 = 4 #

# x = 4; y = 2 (4 / 2-2) ^ 2-4 = 2 (0) -4 = -4 #

Vertex #(4, -4)#

Svar:

#(4, -4)#

Forklaring:

I betragtning af ligningen, # Y = 2 (x / 2-2) ^ 2-4 #

# Y = 2 (frac {x-4} {2}) ^ 2-4 #

# Y = 1/2 (x-4) ^ 2-4 #

# Y + 4 = 1/2 (x-4) ^ 2 #

# (X-4) ^ 2 = 2 (y + 4) #

Ovenstående ligning viser en lodret parabola med vertex

# (x-4 = 0, y + 4 = 0) #

# (x = 4, y = -4) #

#(4, -4)#