Babynini
  • Babynini
Vertex.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Babynini
  • Babynini
Write the equation in standard form then find and list the vertex, focus, and directrix of the parabola. sketch its graph showing the focus and the directrix.(note: Choose the locations of the coordinate axes and draw them on the grid and choose scales so that your graph is, if possible, about three by three inches in size.) x^2+12x+4y+44=0
Babynini
  • Babynini
@jim_thompson5910 If you have time :)
jim_thompson5910
  • jim_thompson5910
are you able to complete the square for the x terms?

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Babynini
  • Babynini
I'm not sure how.
jim_thompson5910
  • jim_thompson5910
x^2+12x+_____ what goes in the blank to make that a perfect square?
Babynini
  • Babynini
36
jim_thompson5910
  • jim_thompson5910
yep
jim_thompson5910
  • jim_thompson5910
so add and subtract 36 on the same side or add 36 to both sides
jim_thompson5910
  • jim_thompson5910
then group (x^2-12x+36) and factor that to get (x-6)^2
Babynini
  • Babynini
kks, I chose to add 36 to both sides (x-6)^2+4y+44=36
Babynini
  • Babynini
(x-6)^2+4y=-8 (subtracted 44 from both sides)
jim_thompson5910
  • jim_thompson5910
now isolate y
Babynini
  • Babynini
y=-(x-6)^2/4 - 8/4
jim_thompson5910
  • jim_thompson5910
yes
jim_thompson5910
  • jim_thompson5910
you can simplify that further
Babynini
  • Babynini
2 instead of 8/4 :P
Babynini
  • Babynini
hrm the original and that one don't graph the same o.0
Babynini
  • Babynini
http://www.wolframalpha.com/input/?i=x%5E2%2B12x%2B4y%2B44%3D0 Original
Babynini
  • Babynini
http://www.wolframalpha.com/input/?i=Parabola+y%3D%28%28x-6%29%5E2%29%2F4%29+-2 New equation
Babynini
  • Babynini
Would it work to do: 4y=-x^2-12x-44 y= -x^2/4 -3x -11 ?
Babynini
  • Babynini
Or does the equation we previously made look better?
Babynini
  • Babynini
http://www.wolframalpha.com/input/?i=Parabola+y%3D-1%2F4x%5E2+-3x-11 ....haha what.
jim_thompson5910
  • jim_thompson5910
let me check
Babynini
  • Babynini
kks
jim_thompson5910
  • jim_thompson5910
oh I made a mistake, it's not -12x it's +12x
jim_thompson5910
  • jim_thompson5910
so it should factor to (x+6)^2
jim_thompson5910
  • jim_thompson5910
you should get \[\Large y = -\frac{1}{4}(x+6)^2 - 2\]
Babynini
  • Babynini
Yep that's what I have :)
Babynini
  • Babynini
that is still a different graph than the original
jim_thompson5910
  • jim_thompson5910
I have it matching up
Babynini
  • Babynini
oh yeah, sorry. It is. Wolfram was doing a close up of the graph and I hadn't noticed.
jim_thompson5910
  • jim_thompson5910
you forgot the negative in http://www.wolframalpha.com/input/?i=Parabola+y%3D%28%28x-6%29%5E2%29%2F4%29+-2
Babynini
  • Babynini
ah, sorry.
Babynini
  • Babynini
so next is finding foci, vertex, and directrix.
jim_thompson5910
  • jim_thompson5910
have a look at this http://www.mathwords.com/f/focus_parabola.htm
Babynini
  • Babynini
k, so mines a vertical parabola.
jim_thompson5910
  • jim_thompson5910
yes
Babynini
  • Babynini
um and I use x^2=4py to find everything?
jim_thompson5910
  • jim_thompson5910
Convert \[\Large y = -\frac{1}{4}(x+6)^2 - 2\] to 4p(y-k) = (x-h)^2 form
Babynini
  • Babynini
would that be (y+2)/4=(x+6)^2 ??
jim_thompson5910
  • jim_thompson5910
more like -4(y+2) = (x+6)^2
jim_thompson5910
  • jim_thompson5910
-4(y+2) = (x+6)^2 is in the form 4p(y-k) = (x-h)^2 p = -1 h = -6 k = -2
Babynini
  • Babynini
ahh ok
jim_thompson5910
  • jim_thompson5910
|dw:1433470391325:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1433470408839:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1433470431794:dw|
Babynini
  • Babynini
f: = (-6,-3)
jim_thompson5910
  • jim_thompson5910
yes
Babynini
  • Babynini
d: y = - 3
jim_thompson5910
  • jim_thompson5910
no
Babynini
  • Babynini
k-p ?
Babynini
  • Babynini
oh sorry, -1
jim_thompson5910
  • jim_thompson5910
yeah directrix is y = -1
anonymous
  • anonymous
hi can i borrow jim_thompson5910
anonymous
  • anonymous
?
Babynini
  • Babynini
umm so the graph looks like |dw:1433470684289:dw|
Babynini
  • Babynini
|dw:1433470710284:dw|
Babynini
  • Babynini
|dw:1433470757831:dw| ish lol
Babynini
  • Babynini
the prof loves complete accuracy. so if I wanted to find the exact points that the parabola passes though do I just substitute numbers for x into the equation and find out y?
jim_thompson5910
  • jim_thompson5910
yeah you can do that to plot points or use desmos to get an accurate graph desmos.com/calculator
jim_thompson5910
  • jim_thompson5910
https://www.desmos.com/calculator
Babynini
  • Babynini
well, i've got to show work. but i'll use desmos to make sure :) thanks!
Babynini
  • Babynini
er it worked until I got to -7 and -8 values for x :o

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