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chrisdbest
 one year ago
Help!!
chrisdbest
 one year ago
Help!!

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chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 7).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so.. the vertex is a the origin the focus point is a 0. 7 care to draw those two in a cartesian plane?dw:1437175007773:dw

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0Vertex is at origin, and focus point is at 0, 7 like you said

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok... so what are the coordinates for the origin?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeap so dw:1437175183982:dw so.... if the parabola makes a Uturn at the 0,0 and the focus is below the vertex that means the parabola is dw:1437175290874:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so is a parabola that opens vertically meaning the "x" term is the one that's squared so \(\bf \begin{array}{llll} (y{\color{blue}{ k}})^2=4{\color{purple}{ p}}(x{\color{brown}{ h}}) \\ (x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\\ {\color{purple}{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\ \quad \\\\ \quad \\ \textit{so we'd need to use this form }(x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now... what is the distance "p", that is, from the vertex to the focus point?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437175751363:dw

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0Wouldn't that be 7?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeap so p is 7 the parabola is going downards, that means "p" is negative so "p" is really negative 7 or 7 so now you know what "p" is, and where the vertex is at, that is what "h" and "k" are so just plug them in at \(\begin{array}{llll} (x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ 0}},{\color{blue}{ 0}})\\ {\color{purple}{ 7}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\) and simplify and solve for "y" :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well... negative 7 rather \(\begin{array}{llll} (x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ 0}},{\color{blue}{ 0}})\\ {\color{purple}{ 7}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\)

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0Ohk, yeah, I meant down 7

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0So what do I do next?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you shall... plug in those values simplify and solve for "y" :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \begin{array}{llll} (x{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y{\color{blue}{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({\color{brown}{ 0}},{\color{blue}{ 0}})\\ {\color{purple}{ 7}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\) notice.... you have all the values you need, just plug them in and solve for "y"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0look at the colors, h,k are just the vertex coordinates

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0Then what does x equal?

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0Ohhh. wait I think I see

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0My answer choices are... A. \[y = \frac{ 1 }{ 7 }x^2\] B. \[y^2 = 7x\] C. \[y=\frac{ 1 }{ 28 }x^2\] D. \[y^2 = 28x\]

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0So I would choose D?

chrisdbest
 one year ago
Best ResponseYou've already chosen the best response.0OMG!!! It's not D!!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Answer is C note the parabola opens down, so its of the form y = x^2 the "y" is squared only if parabola is sideways or opens left/right
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