Question

What is the directrix of the parabola given by the equation y = –5x2 + 60x – 176?

Answer 1

convert to (x-h)^2=4p(y-k) form
(h,k) is vertex
p is distance from vertex to directrix and from vertex to focus
if p is negative, then it opens down (directix is above vertex and focus)
if p is positive, then it opens up (directix is below vertex and focus)
complete the square for x
y=-5(x^2-12x)-176
y=-5(x^2-12x+36-36)-176
y=-5((x-6)^2-36)-176
y=-5(x-6)^2+180-176
y=-5(x-6)^2+4
minus 4 both sides
y-4=-5(x-6)^2
divide both side by -5
(-1/5)(y-4)=(x-6)^2
(4)(-1/20)(y-4)=(x-6)^2
vertex is (6,4)
negative so opens down, directix is 1/20 units down from (6,4)
4 is up and down so 4-1/20=3.95
the directix is (6,3.95)

Answer 2

The directrix of the parabola given by the equation y = –5x2 + 60x – 176 is y = 4 1/20 because finishing the square will give us y = -5(x^2 - 12x + 36) + 180 - 176 = -5(x-6)^2 + 4. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.