Need !
11. the equation of a parabola is given
y= -1/6x^2 + 7x - 80
what is the equation of the directrix of the parabola ?

Since x term is squared, solve for form (x-h)^2=4p(y-k)
x term is squraed so it opens down or up

vertex is (h,k)
p is distance from vertex to focus and from vertex to directix
if p>0, then dirextix is below vertex
if p<0, directix is above vertex

complete the square

y=(-1/6x^2+7x)-80
y=(-1/6)(x^2-42x)-80
take 1/2 of linear coefient and squer it and add negative and positive inside
-42/2=-21, (-21)^2=441
y=(-1/6)(x^2-42+441-441)-80
factor perfect square the square
y=(-1/6)((x-21)^2-411)-80
expand
y=(-1/6)(x-21)^2+73.5-80
y=(-1/6)(x-21)^2-6.5
add 6.5 to both sid
y+6.5=(-1/6)(x-21)^2
times both sides by -6
-6(y+6.5)=(x-21)^2
(x-21)^2=-6(y+6.5)
(y-21)^2=4(-3/2)(y-(-6.5))
vertex is
-3/2<0 so directix is above
it is -3/2 or 1.5 units above the vertex
up is y so
-6.5+1.5=-5
the directix is y=-5