Was sind der Scheitelpunkt, der Fokus und die Directrix von y = x ^ 2-3x + 4?

Antworten:

# "vertex =" (1.5,1.75) #

# "focus =" (1.5,2) #

# "directrix: y = 1,5 #

# y = a (x-h) ^ 2 + k "die Scheitelpunktform der Parabel" #

# "vertex =" (h, k) #

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

# y = x ^ 2-3x + 4 "Ihre Parabelgleichung" #

# y = x ^ 2-3xcolor (rot) (+ 9 / 4-9 / 4) + 4 #

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

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

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

# "vertex =" (1.5,1.75) #

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

# "Fokus =" (1,5,7 / 4 + 1 / (4 * 1)) = (1,5,8 / 4) #

# "focus =" (1.5,2) #

# "Finde directrix:" #

# "Einen Punkt (x, y) auf Parabel nehmen" #

# "let" x = 0 #

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

# y = 4 #

# C = (0,4) #

# "Entfernung zum Fokus finden" #

# 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 #