Question

I need help...
I know there is a transformation
I need help
Find an expression for the function whose graph is the given curve.
The bottom half of the parabola x + (y − 9)2 = 0

Answer 1

ok let me try

Answer 2

no. sorry. my bad. don't

Answer 3

ok

Answer 4

how to do this then...

Answer 5

\[ x + (y − 9)^2 = 0 \] solve for \(y\)
\[(y-9)^2=-x\]
\[y-9=\pm\sqrt{-x}\]
\[y=\pm\sqrt{-x}+9\] but since you are taking the bottom half use the negative square root
\[y=-\sqrt{-x}+9\]

Answer 6

thanks @satellite73

Answer 7

I can't help, but found a similar question:
http://www.freemathhelp.com/forum/archive/index.php/t-54875.html?s=81349e7c156e89af0e48100743b7ef6d
and
http://www.freemathhelp.com/forum/archive/index.php/t-59101.html?s=81349e7c156e89af0e48100743b7ef6d

their q was: Graphing a parabola: only getting half of x = y^2 - 4

solution:

y = \sqrt{x+4} is the top "half" of the parabola (the positive side)

y = -\sqrt{x+4} will give you the bottom half (the negative side)

in function mode, the calculator cannot graph both at the same time using only one function (the entire parabola is not a function, correct?) ... so, put the expression for the positive side in Y1 and the one for the negative side in Y2 ... the calculator graphs two distinct functions and gives you the graph of the "whole" parabola sitting on its side.

Answer 8

nvmd, just saw @satellite73 , follow the guru, whay better explaniation

Answer 9

thanks @Jack1

Answer 10

@satellite73 what will the graph look like? will it have a vertical shift 9 units down?

Answer 11

if it helps to graph it: use y = 9 - i (sqrt x) ... i think

Answer 12

it is only a point

Answer 13

that is showing

Answer 14

click on "real valued plot" to get rid of the complex part
http://www.wolframalpha.com/input/?i=y%3D-sqrt%28-x%29%2B9+domain+-infty..0

Answer 15

https://www.google.com.au/search?q=graph+y+%3D+9-sqrt(-x)&aq=f&oq=graph+y+%3D+9-sqrt(-x)&aqs=chrome.0.57.4046&sourceid=chrome&ie=UTF-8

this is the real part of the line graphed... increases up to y=9 at x = 0, then remains constant i think...
but there's also an imaginary part...

Answer 16

so the graph of the function will be like this: