anonymous
  • anonymous
How would a person graph y=1/2(x+4)^2-5 and find the foci and focus?
Mathematics
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anonymous
  • anonymous
How would a person graph y=1/2(x+4)^2-5 and find the foci and focus?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
No foci http://www.wolframalpha.com/input/?i=focus+y%3D1%2F2%28x%2B4%29^2-5
anonymous
  • anonymous
right but how does a person get -4, -0/2?
anonymous
  • anonymous
-4, -9/2?

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anonymous
  • anonymous
on the websouce is it given as a result
anonymous
  • anonymous
?
anonymous
  • 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
anonymous
  • anonymous
makes sense thanx!
anonymous
  • 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

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