Take Home 5 Math 1500 For the parabola y 8y 4x 0 find the ve

Take Home 5 Math 1500 For the parabola y -8y +4x 0 find the vertex, focus, axis of symmetry, directrix of the latus rectum. Then graph the parabola showing all its features. and vertices

Solution

y²-8y+4x=0

y²-8y+16+4x=16

(y-4)²+4x=16

4x=-(y-4)²+16

x=(-1/4)(y-4)²+16

Here vertex (h,k) =(4,16)

focus(h+1/4a,k) =(3,16)

directrix, x=h-1/4a

x= 4+1=5

Axis of symmetry , y-4=0

y=4