Question

How would a person graph
y=1/2(x+4)^2-5 and find the foci and focus?

Answer 1

No foci
http://www.wolframalpha.com/input/?i=focus+y%3D1%2F2%28x%2B4%29^2-5

Answer 2

right but how does a person get -4, -0/2?

Answer 3

-4, -9/2?

Answer 4

on the websouce is it given as a result

Answer 5

?

Answer 6

okay the standard equation is given by
\[(x-h)^2=4p(y-k)\] lets convert your equation into the standard form
\[y=\frac{1}{2}(x+4)^2-5\Rightarrow (y+5) = \frac{1}{2}(x+4)^2\Rightarrow 2(y+5)=(x+4)^2\] Now we have the equations looking alike
\[(x-h)^2=4p(y-k)\]
\[(x+4)^2=2(y+5)\]
\[-h=4 \rightarrow h=-4 \text{ and 4p = 2 so p = }\frac{1}{2}\text{ and -k=5 so k = -5}\]
\[\text{The focus is given by (h,k+p)}\Rightarrow \text{(-4, -5+}\frac{1}{2}\text{)}\Rightarrow (-4, -\frac{9}{2})\]
hope that helps

Answer 7

makes sense thanx!

Answer 8

p is the directrix,
directrix is line that runs perpendicular to axis of symmetry of parabola
distance to focus equals distance to directrix <--- definition of parabola