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anonymous
 one year ago
What is the equation of the quadratic graph with a focus of (2, 0) and a directrix of y = −12?
anonymous
 one year ago
What is the equation of the quadratic graph with a focus of (2, 0) and a directrix of y = −12?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437691840404:dw any ideas where those two fellas are in the graph? can you graph them there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437691171977:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeap we also know that the vertex is equidistant from both meaning, the focus point is away from the vertex, the same amount the directrix is away from the vertex let's call that distance "p" so, that means the vertex is "halfway" between the focus and directrix the parabola opens towards the focus, the focus is above the directrix, in this case the parabola opens upwards then dw:1437692110933:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the distance from the focus to the vertex is 7, the distance from the directrix to the vertex is 7 the parabola is opening upwards, so the distance "p" is positive the squared variable is the "x" then now that we know where the vertex coordinates are at, and the "p" distance then \(\large \begin{array}{llll} (x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\\ {\color{purple}{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\) plug in your values, and solve for "y"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't the focus be on the xaxis, not the yaxis? since it is (2,0) not (0,2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmmm hold the mayo.. .maybe .... I did mess up there, lemme recheck that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437692548026:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0anyhow, the vertex is halfway, so that makes it a 0,6 and yes, that makes the "p" distance to 6 only \(\begin{array}{llll} (x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ 0}},{\color{blue}{ 6}})\\ {\color{purple}{ 6}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmm wait a sec.. dohh. the x coordinate can't be 0 anyhow hehe one sec

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437692768286:dw \(\begin{array}{llll} (x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ 2}},{\color{blue}{ 6}})\\ {\color{purple}{ 6}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, we have the vertex, now what do we do to get the equation for it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just plug in the values in the parabola equation focus form

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it ends up as (x2)^2 = 4*6(y(6))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeap or \(\bf (x{\color{brown}{ 2}})^2=4{\color{purple}{ (6)}}(y{\color{blue}{ (6)}})\implies (x2)^2=24(y+6) \\ \quad \\ (x2)^2=24y+144\implies \cfrac{(x2)^2144}{24}=y\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is there another way to write that out, because none of the above are answer choices

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I guess one could distribute the denominator, and end up with \(\cfrac{(x2)^2144}{24}=y\implies \cfrac{(x2)^2}{24}\cfrac{\cancel{144}}{\cancel{24}}=y\implies \cfrac{(x2)^2}{24}6=y\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you could also, expand the squared binomial, and simplify it with the 144, and then distribute the denominator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my anwer choices are x^2435; x^2+4+35; 1/24x^2+1/6x35/6; and 1/24x^21/635/6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf \cfrac{(x2)^2144}{24}=y\implies \cfrac{[x^24x+4]144}{24}=y \\ \quad \\ \cfrac{x^24x+4144}{24}=y\implies \cfrac{x^24x140}{24}=y \\ \quad \\ \cfrac{x^2}{24}\cfrac{4x}{24}\cfrac{140}{24}=y\implies \cfrac{1}{24}x^2\cfrac{\cancel{4}}{\cancel{24}}x\cfrac{\cancel{140}}{\cancel{24}}=y\implies ?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0any... thing.. that confuses there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what happens to the second and third fractions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah... whatever happens to those? so... simplify them, what do you get for the simplification? or 4/24 and 140/24?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, ok. The would simplify to 2/12 and 35/8

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well... 2/12 = 1/6 and.... 140/24 simplifiefs to 35/6 thus \(\bf \cfrac{x^2}{24}\cfrac{4x}{24}\cfrac{140}{24}=y\implies \cfrac{1}{24}x^2\cfrac{\cancel{4}}{\cancel{24}}x\cfrac{\cancel{140}}{\cancel{24}}=y \\ \quad \\ \cfrac{1}{24}x^2\cfrac{1}{6}x\cfrac{35}{6}=y\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, ok. Thanks for the help
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