Chapter 10 - Parametric Equations and Polar Coordinates - 10.5 Exercises - Page 700: 25

Parabola Focus: $(0,-\frac{3}{4})$ Vertex: $(0,-1)$

$x^{2}=4py$ is the equation of a parabola with vertex $(0,0)$ and focus $(0,p)$ . Consider the parabola $x^{2}=y$ Thus, Equation of a parabola can be re-written as $x^{2}=4(\frac{1}{4})y$ Focus: $(0,\frac{1}{4})$ Vertex is: $(0,0)$ If we shift this parabola by 1 unit downward, we will get $x^{2}=y+1$ The focus and vertex changes to: Focus: $(0,-\frac{3}{4})$ Vertex: $(0,-1)$