Find the vertex focus and directrix of the parabola Graph th

Find the vertex, focus and directrix of the parabola. Graph the equation. Y^2 + 6y= 4x + 15

Solution

given parabola y²+6y =4x+15

y²+6y+9 =4x+15+9

(y+3)²=4x+24

(y+3)²=4(x+6)

(y-(-3))²=4(x-(-6))

vertex = (-6,-3)

4a =4

=>a=1

focus = (-6+1,-3)

focus = (-5,-3)

directrix is x =-6-1

directrix is x =-7