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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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jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1dw: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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1yeap 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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1the 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)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1hmmmm hold the mayo.. .maybe .... I did mess up there, lemme recheck that

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437692548026:dw

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1anyhow, the vertex is halfway, so that makes it a 0,6 and yes, that makes the "p" distance to 6 only \(\begin{array}{llll} (x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ 0}},{\color{blue}{ 6}})\\ {\color{purple}{ 6}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1hmmm wait a sec.. dohh. the x coordinate can't be 0 anyhow hehe one sec

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1dw: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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1just 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))

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1yeap 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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1I guess one could distribute the denominator, and end up with \(\cfrac{(x2)^2144}{24}=y\implies \cfrac{(x2)^2}{24}\cfrac{\cancel{144}}{\cancel{24}}=y\implies \cfrac{(x2)^2}{24}6=y\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1you 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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1\(\bf \cfrac{(x2)^2144}{24}=y\implies \cfrac{[x^24x+4]144}{24}=y \\ \quad \\ \cfrac{x^24x+4144}{24}=y\implies \cfrac{x^24x140}{24}=y \\ \quad \\ \cfrac{x^2}{24}\cfrac{4x}{24}\cfrac{140}{24}=y\implies \cfrac{1}{24}x^2\cfrac{\cancel{4}}{\cancel{24}}x\cfrac{\cancel{140}}{\cancel{24}}=y\implies ?\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1any... thing.. that confuses there?

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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1yeah... 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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1well... 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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