SOLUTION: Find the vertex, focus and directrix of the parabola y= -3x^2+12x-8 without completing the square and determine whether the parabola opens upward or downward

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the vertex, focus and directrix of the parabola y= -3x^2+12x-8 without completing the square and determine whether the parabola opens upward or downward       Log On


   

Question 849018: Find the vertex, focus and directrix of the parabola y= -3x^2+12x-8 without completing the square and determine whether the parabola opens upward or downward
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

 y= -3x^2+12x-8

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-12+%2B-+sqrt%28+48%29%29%2F-6%29+

x+=+%28-12+%2B-+sqrt%28+16%2A3%29%29%2F-6%29+

 x+=+2+%2B-++%28-2%2F3+%29sqrt%283%29

  midpoint =%28%282+-+%282%2F3%29sqrt%283%29%29+%2B+%282%2B%282%2F3%29sqrt%283%29%29%29%2F2+ = 2  0r simply x+=+-b%2F2a%29%29%29%0D%0AV%282%2C4%29+%28Substituting+x+=+2+%7B%7B%7B-12%2B24-8+=+4

Parabola Opening downward:  +y=+green%28-3%29x%5E2%2B12x-8 

1%2F%284a%29+=+-1%2F12, 4 + (-1/12) = 47/12 Focus(2,47/12)

directrix is y = 4+1/12 = 49/12