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anonymous
 one year ago
I'm new to this website and how it works, but I would appreciate it if somebody helped me!
Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = 7.
anonymous
 one year ago
I'm new to this website and how it works, but I would appreciate it if somebody helped me! Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = 7.

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PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1What did you notice when you graphed these two points on a plane?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Phantomcrow It opens to the right?

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Yes! And you know what the standard equation of a parabola that opens to the right is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Phantomcrow Can you help me out with that one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It is 3, you're welcome.

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Sure.dw:1444091089825:dw

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Since the vertex is at the origin, there is no need to add any constants for shifts. The graph is simply \[y^2=x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Phantomcrow By the way the Answer choices are y= 1/28x^2 x= 1/28y^2 28y= x^2 y^2=14x What confuses me is how these tie to the standard formula

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1D. Despite it having an 'x' term, its vertex is still at the origin.

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Standard form is one of the ways to write the graph of a parabola. It is commonly seen as:\[ax^2+bx+c\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Phantomcrow Wow thanks, would it be cool if you helped me with one more?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Phantomcrow Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = 8, i'm guessing this is similar or even exact to the last one, so it opens to the left

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Actually, it does not open to the left this time. You are given y values for focus and directrix, not x values.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Phantomcrow So y values open to the right and x values open to the left?

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Y values lie across a vertical line, you your parabola will be opening upwards. You can easier see this if you look at the (0.8) and y= 8 on a graph. See that the they are equidistant from a point.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@PhantomCrow you graph (0,8) correct?

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Yes. Graph the point (0,8) and y= 8 and you should be able to visually see the the point that is equidistant from them. There is a formula for finding distance but I believe simply looking at the graph for this problem will provide you with the answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@PhantomCrow The choices are y= 1/32x^2 y^2= 8x y^2=32x y=1/8x^2 Would it be B?

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Well, you have two possible answers. A and D. B and C are ruled out because that would be a parabola who's focus is (x,0) and directrix is x=something. We have a focus like (0,y) and y=something in this case so its not y^2=x

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Since you need to figure out which is correct between A and D, your best method is to plug in what you know into vertex form (\[(xh)^2=4p(yk)\] where (h, k) is the vertex and p is the distance from either the directrix or the focus to the vertex.

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1We know that the vertex lies at (0,0) because that is the point equidistant from (0,8) and y=8. P is not difficult to find. P is just 8 because the distance from either the directrix or the focus to the vertex is 8 units (if you need the formula, just ask, but its not necessary).

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1Plug that into the vertex form:\[(xh)^2=4p(yk)\] \[(h,k)=(0,0)\] so \[h=0, k=0\] \[(x0)^2=4(8)(yk)\] \[x^2=32y\] \[\frac{ x^2 }{ 32 }=y\]

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1We want it in terms of y because that's how standard form is written. So we solved for y.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@PhantomCrow Which will result in y=1/32x^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@PhantomCrow Thank you so much for your help have a blessed day!

PhantomCrow
 one year ago
Best ResponseYou've already chosen the best response.1No problem, you as well.
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