Question

please help!
find the vertex, focus,and directrix of the parabola and sketch its graph
(x+3/2)^2=4(y-2)

Answer 1

rewrite it as
\[ y = \frac 14 (x+3/2)^2 + 2\]
put, x=-3/2, y = 2 , this is your vertex

Answer 2

http://www.wolframalpha.com/input/?i=plot+%28x%2B3%2F2%29%5E2%3D4%28y-2%29+from+x%3D-5+to+5%2C+y%3D0+to+10

Answer 3

since the parabola is a vertical parabola, the focus is going to be (-3/2,a)

let directrix be y=b