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)
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
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