Chapter 10 - Analytic Geometry - 10.2 The Parabola - 10.2 Assess Your Understanding - Page 647: 42

Vertex: $(0,0)$ Focus: $(0,-1)$ Directrix: $y=1$ See graph

We are given the parabola: $x^2=-4y$ The standard equation is: $(x-h)^2=4p(y-k)$ Determine $h,k,p$: $h=0$ $k=0$ $4p=-4\Rightarrow p=-1$ Determine the vertex: $(h,k)=(0,0)$ Determine the focus: $(h,k+p)=(0,0+(-1))=(0,-1)$ Determine the directrix: $y=k-p$ $y=0-(-1)$ $y=1$ Determine the two points defining the latus rectum: $y=-1$ $x^2=4$ $x=\pm 2$ $\Rightarrow (-2,-1),(2,-1)$ Plot the points, draw the directrix, and graph the parabola: Vertex: $(0,0)$ Focus: $(0,-1)$ Directrix: $y=1$ See graph