Welche quadratische Funktion wird unter Verwendung eines Directrix von y = -2 und eines Fokus von (1, 6) erzeugt? ein. f (x) = (1 / 8) (x-1) ^ 2 - 2 b. f (x) = - (1 / 8) (x + 1) ^ 2 - 2 c. f (x) = - (1 / 16) (x + 1) ^ 2 - 2 d. f (x) = (1 / 16) (x-1) ^ 2 + 2

#"from any point "(x,y)" on the parabola the focus and"#
#"directrix are equidistant"#

#"using the "color(blue)"distance formula"#

#sqrt((x-1)^2+(y-6)^2)=|y+2|#

#color(blue)"squaring both sides"#

#(x-1)^2+(y-6)^2=(y+2)^2#

#(y-6)^2-(y+2)^2=-(x-1)^2#

#cancel(y^2)-12y+36cancel(-y^2)-4y-4=-(x-1)^2#

#-16y+32=-(x-1)^2#

#-16y=-(x-1)^2-32#

#rArry=f(x)=1/16(x-1)^2+2to(d)#