Chapter 4 - 4.4 - Translations of Conics - 4.4 Exercises - Page 347: 27

Vertex: $(1,-2)$ Focus: $(h,k+p)=(1,-4)$ Directrix: $y=0$

Standard form of a parabola with vertical axis, vertex $(h,k)$ and focus $(h,k+p)$ $(x-h)^2=4p(y-k)$ $(x-1)^2+8(y+2)=0$ $(x-1)^2=-8(y+2)$ $h=1$ and $k=-2$ Vertex: $(1,-2)$ $4p=-8$ $p=-2$ Focus: $(h,k+p)=(1,-2+(-2))=(1,-4)$ Directrix: $y=k-p=-2-(-2)=0$