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anonymous
 one year ago
Regan is trying to find the equation of a quadratic that has a focus of (−2, 5) and a directrix of y = 13. Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand.
anonymous
 one year ago
Regan is trying to find the equation of a quadratic that has a focus of (−2, 5) and a directrix of y = 13. Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't quite understand how to find a when writing the equation.. that's all I need help with.

jchick
 one year ago
Best ResponseYou've already chosen the best response.1Sorry it took so long to reply lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I waited till I saw you weren't actively helping someone

jchick
 one year ago
Best ResponseYou've already chosen the best response.1The definition of a parabola is that the distance of any point on it from the focus is equal to the distance of the point from the directrix. So if (x,y) is a point on the parabola, then find the distance of (x,y) from the focus (2,5). Find the distance of (x,y) from y = 13. Equate them and you will have your quadratic equation.

jchick
 one year ago
Best ResponseYou've already chosen the best response.1(x+2)^2+(y−5)^2=(y−13)^2 Simplify above.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but how do you find (x,y)?

jchick
 one year ago
Best ResponseYou've already chosen the best response.1no matter what value x is, y will always be 13

jchick
 one year ago
Best ResponseYou've already chosen the best response.1directrix y = 13 can be represented as the point (x, 13)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay, that makes sense.

jchick
 one year ago
Best ResponseYou've already chosen the best response.1So after inputting the points, you have: (x−(−2))2+(y−5)2−−−−−−−−−−−−−−−−−−√=(x−x)2+(y−13)2−−−−−−−−−−−−−−−−√

jchick
 one year ago
Best ResponseYou've already chosen the best response.1You can then square both sides to get: (x−(−2))2+(y−5)2= (x−x)2+(y−13)2

jchick
 one year ago
Best ResponseYou've already chosen the best response.1Does this make sense so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im not sure... itdoes a little bit

jchick
 one year ago
Best ResponseYou've already chosen the best response.1Ok where do you need explanation?

jchick
 one year ago
Best ResponseYou've already chosen the best response.1You can then square both sides to get: (x−(−2))^2+(y−5)^2= (x−x)^2+(y−13)^2

jchick
 one year ago
Best ResponseYou've already chosen the best response.1sorry that is the correct version

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what are you plugging them into?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0like are you plugging those into an equation??

jchick
 one year ago
Best ResponseYou've already chosen the best response.1And then that simplifies to (x+2)^2+(y−5)^2=(y−13)^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, what equation?

jchick
 one year ago
Best ResponseYou've already chosen the best response.1(x−(−2))2+(y−5)2−−−−−−−−−−−−−−−−−−√= (x−x)2+(y−13)2−−−−−−−−−−−−−−−−√

jchick
 one year ago
Best ResponseYou've already chosen the best response.1inserted points (2,5) and (x, 13) the distance formula: (x−x1)2+(y−y2)2−−−−−−−−−−−−−−−−−√=(x−x2)2+(y−y2)2−−−−−−−−−−−−−−−−−√

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0like I was learning it like this... The graph of the quadratic is a parabola. The directrix is horizontal, so the parabola is vertical. The focus lies below the directrix, so the parabola opens downwards. General equation of a downopening parabola: y = a(x  h)² + k with a < 0 vertex (h, k) focal length p =  1/(4a)  focus (h, kp) directrix y = k+p Plug your data into the equations and solve for a now im really confused... when I was only confused about how to figure out what a is XD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its cool I just didn't know what you were plugging it all into.. XD

jchick
 one year ago
Best ResponseYou've already chosen the best response.1Having internet trouble please hang on a second

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I've never seen this done this way. Pretty cool @jchick It looks like this is using the definition of a parabola as the set of points equidistant between the focus and directrix. A circle is a set of point equidistant from the same point. The equation for a circle is \[(xh)^2+(yk)^2=r^2\]. jchick set the equations for 2 circles equal to each other, one for the focus with (2, 5) and the other for the directrix (x, 13). That's where this came from \[(x+2)^2+(y5)^2=(xx)^2+(y13)\] If you mulitply everything out, and then complete the square you can find a with this method

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so do you use the distance formula to find a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that's pretty much what it works out to being. and you don't actually need to complete the square. a will be the coefficient of x²

jchick
 one year ago
Best ResponseYou've already chosen the best response.1Sorry I am back and thank you @peachpi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just FOIL out the equation and you'll have an expanded equation for the parabola

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im still really confused... what is r in that equation??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Maybe try a different method since this is confusing. We know that the vertex is halfway between the focus and directrix, so it's (2, 9) and the parabola opens down like you said above. So the focal length is 9  5 = 4 dw:1439944412409:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do you find the vertex?

jchick
 one year ago
Best ResponseYou've already chosen the best response.1(xa)^2 =4p(yb) vertex =(a,b)

jchick
 one year ago
Best ResponseYou've already chosen the best response.1@kaylamarie79 do you remember the standard form?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The parabola opens down so the vertex has to be directly above the focus, meaning the xcoordinate has to be 2. The vertex is halfway between focus and directrix, so it's halfway between 5 and 13, so the ycoordinate has to be 9. Vertex = (2, 9). To find a: From your list of equations above, \[p=\left \frac{ 1 }{ 4a } \right\] Since you know p, you can solve for a.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@peachpi I dont know p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0p is the focal distance

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0p = distance from vertex to focus = distance from vertex to directrix = half the distance from focus to directrix

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01 min im trying wrap my mind around this..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what are you thinking?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0all I can think is i'm sooo confused... like I don't understand where your getting a the focal point(p) or the vertex... and I keep getting more confused as y'all repeat things.. like i'm terrible in math and have to see every single step or the entire equation gets jumbled around in my head...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok. starting from the beginning. The directrix is y = 13. The focus is (2, 5).dw:1439945735884:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The vertex has to be halfway between them. 9 is halfway between 5 and 13, so the vertex has to be (2, 9)dw:1439945891758:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do you get the vertex point?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what number is halfway between 5 and 13?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay. how do you know the 2 though?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because the parabola opens down, the focus and vertex must have the same xcoordinate

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it always equal as the focus or only when opening down?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0only when opening up or down. When it opens left or right the ycoordinates are the same

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay that makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that's the vertex. Now for p. That's the distance between the focus and vertex, so it's p = 9  5.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, so to get a you use the focal length equation but just plug in p?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes. but since it opens down make p be 4 and you can drop the absolute value signs

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhhhh see the other ways just got really confusing..

jchick
 one year ago
Best ResponseYou've already chosen the best response.1Did you find your answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, I did.., I understand now XD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you guys for helping

jchick
 one year ago
Best ResponseYou've already chosen the best response.1Yeah no problem and sorry about being confusing lol
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