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garcia36
20.07.2019 •
Mathematics
Someone i am so desperate like actually crying 1. the equation of a parabola is given. y=−1/6x2+7x−80 what is the equation of the directrix of the parabola? 2. (y+2)^2= 129x-5) what is the equation of the directrix of the parabola?
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Ответ:
we have that
y=−1/6x2+7x−80
y= (−1/6)x^2+7x−80 multiply both sides by -6
-6y = x^2 - 42x + 480 subtract 480 from both sides
-6y - 480 = x^2 - 42x take (1/2) of 42 = 21square this = 441 and add to both sides
-6y - 480 + 441 = x^2 - 42x + 441 simplify the left, factor the right
-6y - 39 = (x - 21)^2 factor the left side as
-6 (y + 39/6) = ( x - 21)^2 (1)
Using the form
4p (y - k) = ( x - h)^2 we can write (1) as
4 (-3/2)(y - (-39/6) ) = ( x - 21)^2
The vertex = ( h, k) = ( 21, -39/6) and p = -3/2
And the directrix is given by
y = k - p → y = -39/6 - (-3/2) = -39/6 + 3/2 = -39/6 + 9/6 =
-30/6 = - 5> y=-5
the answer Part 1) is
y=-5
Part 2) (y+2)^2= 129X-5
What is the equation of the directrix of the parabola?(y+2)²= 129X-5 > 129*(x-5/129)=(y+2)² (1)
Using the form
4p (x - h) = ( y - k)^2 we can write (1) as
4*(129/4)*(x-5/129)=(y+2)²
The vertex = ( h, k) = ( 5/129, -2) and p = 129/4
And the directrix is given by
x = h - p → x = 5/129 - (129/4) = (20-16641)/516> -16621/516
x=-32.21
the answer part 2) is
x=-32.21Ответ:
6.1
Step-by-step explanation:
109.8 divided by 18