Hvad er vertex, fokus og directrix af y = x ^ 2-3x + 4?

Svar:

# "Toppunkt =" (1.5,1.75) #

# "Fokus =" (1.5,2) #

# "directrix: y = 1,5 #

# y = a (x-h) ^ 2 + k "vertexformen af parabola" #

# "Toppunkt =" (h, k) #

# "Fokus =" (h, k + 1 / (4a)) #

# y = x ^ 2-3x + 4 "din parabola ligning" #

# Y = x ^ 2-3xcolor (rød) (+ 9 / 4-9 / 4) + 4 #

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

# Y = (x-3/2) ^ 2 + 7/4 #

# "Toppunkt" = (h, k) = (3 / 2,7 / 4) #

# "Toppunkt =" (1.5,1.75) #

# "Fokus =" (h, k + 1 / (4a)) #

# "Fokus =" (1.5,7 / 4 + 1 / (4 * 1)) = (1.5,8 / 4) #

# "Fokus =" (1.5,2) #

# "Find directrix:" #

# "tag et punkt (x, y) på parabola" #

# "lad" x = 0 #

# Y = 0 ^ 2-3 * 0 + 4 #

# Y = 4 #

# C = (0,4) #

# "find afstand til fokus" #

# J = sqrt ((1.5-0) ^ 2 + (2-4) ^ 2) #

# J = sqrt (2,25 +4) #

# J = sqrt (6,25) #

# J = 2,5 #

# Directrix = 4-2,5 = 1,5 #

# Y = 1,5 #