Answer:
The equation of the quadratic graph is f(x)= - (1/8) (x-3)^2 + 6 (second option)
Step-by-step explanation:
Focus: F=(3,4)=(xf, yf)→xf=3, yf=4
Directrix: y=8 (horizontal line), then the axis of the parabola is vertical, and the equation has the form:
f(x)=[1 / (4p)] (x-h)^2+k
where Vertex: V=(h,k)
The directix y=8 must intercept the axis of the parabola at the point (3,8), and the vertex is the midpoint between this point and the focus:
Vertex is the midpoint between (3,8) and (3,4):
h=(3+3)/2→h=6/2→h=3
k=(8+4)/2→k=12/2→k=6
Vertex: V=(h,k)→V=(3,6)
p=yf-k→p=4-6→p=-2
Replacing the values in the equation:
f(x)= [ 1 / (4(-2)) ] (x-3)^2 + 6
f(x)=[ 1 / (-8) ] (x-3)^2 +6
f(x)= - (1/8) (x-3)^2 + 6
