What is the equation of the quadratic graph with a focus of (3, −1) and a directrix of y = 1?
a.) f(x) = −one fourth (x − 3)2 + 1
b.) f(x) = −one fourth (x − 3)2
c.) f(x) = one fourth (x − 3)2 + 1
d.) f(x) = one fourth (x − 3)2

Use our brains and what we know
f(x)=a(x-h)²+k
vetex is (h,k)
and a is te leading coefient

if directix is below the focus, then it opens up and a is positive
if directix is above focus, then it opens down and a is negaitve

vertex is in between directix and focus

so
(3,-1) and y=1
-1<1
so directix is above
a is negative

directly in between
distance from -1 to 1 is 2
2/2=1

1 above (3,-1) is (3,0)
vertex is (3,0)

y=a(x-3)²+0
y=a(x-3)²

the only option with a negative 'a' value is B

answer is B