anonymous
  • anonymous
@freckles
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Using a directrix of y = -2 and a focus of (1, 6), what quadratic function is created? f(x) = 1/8(x - 1)2 - 2 f(x) = -1/8(x + 1)2 - 2 f(x) = -1/16(x + 1)2 - 2 f(x) = 1/16(x - 1)2 + 2
freckles
  • freckles
first little drawing: |dw:1433741364872:dw| I'm going to put the vertex midway between that horizontal line (Called y=-2) and the focus point (1,6) We will see if you are able to tell with the vertex point is...
freckles
  • freckles
|dw:1433741453855:dw|

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freckles
  • freckles
the point I labeled V is the vertex it is midway between the directrix (y=-2 ) and the focus can you tell me the coordinates of the V point O have plotted for you
anonymous
  • anonymous
(1, 2)
anonymous
  • anonymous
am i right or am i misunderstanding
freckles
  • freckles
that's right
anonymous
  • anonymous
okay now what?
freckles
  • freckles
|dw:1433741706545:dw| \[4p(y-k)=(x-h)^2 \\ \text{ you said vertex was } (1,2)=(h,k) \\ 4p(y-2)=(x-1)^2 \] now we need to find p is the distance between the vertex and the focus or also the distance between the vertex and the directrix p can be negative or positive depending on which way it is opened ours is opened up so it will be positive
freckles
  • freckles
|dw:1433741880300:dw| this distance is p
anonymous
  • anonymous
so we do \[\frac{ y_2 - y_1 }{ x_2 - x_1 }\] ?
freckles
  • freckles
no
freckles
  • freckles
it is a distance not a slope
anonymous
  • anonymous
oh then is it 4?
freckles
  • freckles
yea
anonymous
  • anonymous
ok
freckles
  • freckles
\[4p(y-2)=(x-1)^2 \\ 4(4)(y-2)=(x-1)^2 \\ 16(y-2)=(x-1)^2 \\ \] divide both sides by 16 and then add 2 on both sides
anonymous
  • anonymous
\[y - 2 = \frac{ (x - 1)^2}{ 16 }\] \[y = \frac{ 2 + (x - 1)^2 }{ 16 }\] like this?
anonymous
  • anonymous
oh so the answer is D
freckles
  • freckles
why does 2 have 16 underneath it ?
freckles
  • freckles
you add 2 on both sides after dividing 16 on both sides
anonymous
  • anonymous
sorry that was a typo
freckles
  • freckles
\[y=2+\frac{(x-1)^2}{16} \\ y=\frac{1}{16}(x-1)^2+2\]
anonymous
  • anonymous
Thanks can you help with a couple more?
anonymous
  • anonymous
ill post them in a new thread so you can get more medals ?
freckles
  • freckles
I actually have to leave here I'm sorry
anonymous
  • anonymous
okay np thnx for the help anyways
freckles
  • freckles
it's 1 am almost I have to wake up early
anonymous
  • anonymous
no don't worry about it your good thanks

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