Graphing shifted parabolas aFind the vertex focus and direct

Graphing shifted parabolas. a)Find the vertex, focus, and directrix of the parabola.    b)sketch a graph showing the parabola and its directrix

x² + 2x - 20y + 41 = 0

Solution

x²+2x -20y +41=0

x²+2x+ 1 -20y=-41+1

(x+1)² +40= 20y

y= (1/20)(x+1)²+2

This is of the form

y=(1/4p)(x-h)²+k

where vertex is (h,k) which is (-1,2) here

focus is (h,k+p)

And here p =5

Therefore focus (-1,7)

Directrix,y=k-p

              y= 2-5=-3

Therefore directrix is , y=-3