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

1. anonymous
2. anonymous

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

3. anonymous

-4, -9/2?

4. anonymous

on the websouce is it given as a result

5. anonymous

?

6. anonymous

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

7. anonymous

makes sense thanx!

8. anonymous

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