+128 The equation of a parabola is given.
y=−1/6x^2+7x−80
What is the equation of the directrix of the parabola?
+129852 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 = 21.....square 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)
Usiing the form
4p (y - k) = ( x - h) we can write (1) as
4 (-3/2)(y - (-39/6) ) = ( x - 21)^2
The vertex = ( x, 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
See the graph, here : https://www.desmos.com/calculator/hqmz4lhcvk
