Does this graph is a parabola or not???

[jos_iqmath2010]

Hi, I have the funtion that appears below, to graph it on my calculus1 test yesterday, I have an IQ of 140 and I am a master of Maths, so resolving the excersice is not the problem I know how to graphic it and all the values; but my question is, does this forms a parabola or not???, because since -2 to 2 it forms a parabola but with -3 to 3 after -2 to 2 forms a short straight line joined to the parabola, so this means that in that point the ''parabola'' change it's direction and after >-3 to >3, I mean -4 to 4, does not exist anymore, because the values become negative inside the squareroot, so they are imaginaries. NOTE: MY NATIVE LANGUAGE IS SPANISH, SO PARDON ME IF I MAKE SOME ORTOGRAPHIC MISTAKES.

IS THIS FUNTION COMPLETE CONSIDERING A PARABOLA OR NOT?

g(x)= 3-sqrt(9-t^2) :?:

values from -3, to 3

Thanks.

 

[jos_iqmath2010]

Hi, I thought it was a good idea to upload another picture of the graph, this time zoomed.

Thanks.

Does this is a complete parabola or not???

g(x)= 3-squareroot(9-t^2) :?:

 

[Deleted member 4993]

Hi, I have the funtion that appears below, to graph it on my calculus1 test yesterday,

I have an IQ of 140 and I am a master of Maths, (Too much Information)

so resolving the excersice is not the problem I know how to graphic it and all the values; but my question is, does this forms a parabola or not???, because since -2 to 2 it forms a parabola but with -3 to 3 after -2 to 2 forms a short straight line joined to the parabola, so this means that in that point the ''parabola'' change it's direction and after >-3 to >3, I mean -4 to 4, does not exist anymore, because the values become negative inside the squareroot, so they are imaginaries. NOTE: MY NATIVE LANGUAGE IS SPANISH, SO PARDON ME IF I MAKE SOME ORTOGRAPHIC MISTAKES.

IS THIS FUNTION COMPLETE CONSIDERING A PARABOLA OR NOT? << No - it is a part of an ellipse

g(x)= 3-sqrt(9-t^2) :?:

values from -3, to 3

Thanks.

Let evaluate plot t=2, t = 2.5 & t = 3

t	           g
2	     0.763932023
2.5	   1.341687605
3	     3

Those points do not make a straight line.

A master of math - taking calculus - should know that!!

 

[lookagain]

[quote="jos_iqmath2010":2ppux8bv]



IS THIS FUN[C]TION COMPLETE CONSIDERING A PARABOLA OR NOT? << No - it is a part of an ellipse

g(x)= 3-sqrt(9-t^2) :?:

values from -3, to 3

[/quote:2ppux8bv]

It is part of an ellipse, BUT it is a special case of (part of) an ellipse. It is also (part of) a circle.
That graph is misleading because the scales {placement of the tick marks) are not the same for each axis.

jos_iqmath2010,

your equation needs to be consistent by having one type of variable in it.

Suggestion:

g(x) = 3 - sqrt(9 - x^2) \(\displaystyle \ \ or \ \ g(x) = 3 - \sqrt{9 - x^2}\)

galactus,

it is not a circle, it is a semicircle. It is the lower half of the circle centered
at (0, 3) and having a radius of 3.

It is not the entire circle as g(x) is assigned no more than one value for each x-value.
A circle is not a function (horizontal line test, for example), and g(x) is a function.
And it is the lower half due to the negative sign in front of \(\displaystyle \sqrt{9 - x^2}.\)

 

[jos_iqmath2010]

Subhotosh Khan:
I think that is not necessarily to be very precise with the values in order to answer my question. First, the straight line is from: x= -2.9aprox y=2.2aprox to x= -3 to y= 3; and from x= 2.9aprox to y=2.2aprox to x=3 to y=3; with these values it forms two separate short straight lines one with the negative x value, and one with the positive x value, both in positive Yaxys; AND OF COURSE I KNOW ALL THIS, so when I said it forms a straight line from -2 to 2 until -3 to 3 I was generalizing in Xaxys in order to enphasis my question, because the exactly values you and I already have it in the graphic values at the right side of the picture; Second, my question was only if is it a complete parabola or not? That's all, the values are not exactly needed because the graphic shape in this case speaks by itself. Finally, if you said ''too much information'' about my IQ etc. Why then you are unfocused about evaluate 2, 2.5, 3 if these values does not makes a straight line, right? What about it, if not only a calculus master but even a elementary school kid know that the entire graph is not a line, and also know that the straight line is just a very small part of the graphic, THAT'S EVEN WHY I UPLOAD ANOTHER IMAGE ZOOMED; and that's something that you ''ELITE'' should ''catch at once'', is not about when start or end the VALUES THAT FORMS those straight lines; it is about that the ''parabola'' CHANGE IT'S DIRECTION AT ''SOME'', ''ANY'' POINTS BUT IT DOES, UNDESTAND THAT it was just a question base on the graphic form, and not to actually resolve or evaluated it??? SO, YOU ALSO GIVE TO MUCH INFORMATION, BECAUSE YOU SHOULD ONLY ANSWER THE QUESTION, LIKE YOU DID: NO IT IS A PART OF AN ELLIPSE. Thanks anyway.

 

[jos_iqmath2010]

lookagain
YOU ARE RIGHT, when you say that IT IS A SPECIAL PART OF PART OF AN ELLIPSE, AND EVEN PART OF A SEMICIRCLE; that's what satisfies my question, thank for your information about this graphic form; because my profesor yesterday told that it was a parabola, but since the begining of the test, to even after, I was telling him that something was really strange with it, and I had the suspicion that it was not a parabola; but I did not know about it was a special case. Also all the other information at the end of your post, I really apreciate it all. BUT ABOUT THE SUGGESTION OF g(x)= 3-squareroot(9-x^2) - I know should be X if say g(x), but that t^2 it was how the professor wrote as in the test, I have to put the same that he did, in order to show him his mistake. Something that I find interesting is that supposedly he took that funtion g(x) wiht the t^2 from Stewar's Calculus book. BUT I AM REALLY DOUBT IT.

THANKS A LOT BY YOUR HELP, A+ .

 

[jos_iqmath2010]

Hi galactus, thanks to your usefull information, here is the above part and both functions g(x) = 3-squareroot(9-x^2) and g(x) = 3+squareroot(9-x^2), that completed the ellipse in the graphic. This support your info about the functions. And this also confirm that this fuctions can not be never a parabola, so I hope my professor consider that ''point'' in my test.

Thanks.