Raymond B. answered • 07/26/22
Math, microeconomics or criminal justice
(y+3)^2 = 8(x-2)
vertex is (2,-3)
general form of the rightward opening parabola is
(1/4p)(y-k)^2 = (x-h) where the vertex is (h,k) = (2,-3)
4p=8, p=2, the distance from the focus to the vertex
and the distance from the directrix to the vertex
the vertex is midway between the focus and directrix
focus is (4,-3)
the focus has the same y coordinate as the vertex: -3
because the parabola opens horizontally
directrix is x=0
the directrix and focus are equidistant from the vertex. each 2 units from the vertex
(x-h)= (1/8)(y-k)^2 where 8=4p,
p = 8/4 =2 = the distance horizontally from the vertex to the focus and from the vertex to the directrix
It helps to plot the points and draw a rough sketch of the parabola
check the solution by plugging in another point on the parabola such as (4,1)
or the nearby x intercept (25/8,0)
the point (4,1) is 4 units directly above the focus and 4 units directly to the right of the directrix
(1+3)^2 = 8(4-2)
(4)^2 = 8(2)
16=16
(0+3)^2 = 8(25/8 -2)
3^2 = 8(9/8)
9 = 9
