the answer
the general formula showing parabola is
y = ax² + bx +c, its standard form is y = a(x-h)² + k
the focus formula is
F(h, k + 1 /4a) and the directrix is
the directrix is V( k - 1/4a)
so he equation of a parabola with (−1, −3) as its focus implies
(h, k + 1 /4a) = (−1, −3)
h =-1, and k + 1 /4a = -3
the directrix is k - 1/4a =1
we should solve the system of equation
k + 1 /4a = -3
k - 1/4a =1
2k= -3+1 = -2, so k =-1 and when we use this value
-1 -1/4a = 1 implies 2 = -1/4a this equation give a = -1/8
finally the equation is
y = -1/8 (x +1)² -1
