Write an equation for each translation of x^2 + y^2 = r^2 with the given radius. Right 5 units, down 3 units; radius 8.

Write an equation of a hyperbola with the given foci and vertices. foci (+-17, 0), vertices (+-8, 0)

therefore

find an equation of a hyperbola with vertices (+4,0), (-4,0) and foci (6,0), (-6,0)

refer to a text for details, but...
,  

so that 

 

and thus... 

y=x^2+2x+1 what is the range of the parabola?

so the range is [0,oo)