Graph   y = -x^2 + 4

Here's a cool animation:

Here's the work:

graph of y = -x^2 + 4

y = -x^2 + 4 ... opens down, standard shape, shifted up 4

 

Graph   y = ( x + 2 )^2 - 1 

The animation:

The work:

graph of y = ( x + 2 )^2 - 1

y = ( x + 2 )^2 -1 ... x = -2 makes this 0^2, standard shape opening up, shifted down 1