Ano ang vertex, focus at directrix ng y = 4x ^ 2 + 5x + 7?

Ibinigay ang equation:

# y = 4x ^ 2 + 5x + 7 #

# y = 4 (x ^ 2 + 5 / 4x) + 7 #

# y = 4 (x ^ 2 + 5 / 4x + 25/64) -25 / 64 + 7 #

# y = 4 (x + 5/8) ^ 2 + 423/64 #

# (x + 5/8) ^ 2 = 1/4 (y-423/64) #

Paghahambing sa itaas ng equation na may pamantayang anyo ng parabola # X ^ 2 = 4aY # nakukuha namin

# X = x + 5/8, Y = y-423/64, a = 1/16 #

Vertex ng Parabola

# X = 0, Y = 0 #

# x + 5/8 = 0, y-423/64 = 0 #

# x = -5 / 8, y = 423/64 #

#(-5/8, 423/64)#

Tumutok sa parabola

# X = 0, Y = a #

# x + 5/8 = 0, y-423/64 = 1/16 #

# x = -5 / 8, y = 427/64 #

#(-5/8, 427/64)#

Directrix ng parabola

# Y = -a #

# y-423/64 = -1 / 16 #

# y = 419/64 #