in vertex form
y=a(x-h)²+k
(h,k) is the vertex
and a is some constant
given that the vertex is (-5,-4)
h=-5, k=-4
y=a(x-(-5))²+(-4)
y=a(x+5)²-4
find a by subsituting the gven point
(1,8)
when x=1, y=8
y=a(x+5)²-4
8=a(1+5)²-4
8=a(6)²-4
8=36a-4
add 4 to both sides
12=36a
divide both sides by 36
1/3=a
so the equation is
[tex]y=\frac{1}{3}(x+5)^2-4[/tex]
that is the first option
