Upside down parabola equation -- needed for a quiz

[gracy]

<[/PLAIN] Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

http://www.chilimath.com/flash-quiz/algebra/intermediate/oef/odd-even-functions-quiz.html
In this quiz I got all correct except 4th question.
I know how to figure out function is odd or even but for that I have to know the function of the graph I know equation of parabola is $f(x)$=$x^2$
but I don't know whether it is applicable for upside down parabola,by upside down parabola I mean parabola of this type

 

[DaveC426913]

What mathematical operator flips a function across its X-axis?

 

[Mister T]

The function you've graphed is a parabola that opens down. It's an even function.

The function graphed in question 4 is a parabola that opens down, but it's not an even function.

Look again at the two graphs.

I know equation of parabola is f(x)=x²

That's the equation of only a parabola that opens up and has its vertex at (0,0).

 

[SammyS]

...

The function graphed in question 4 is a parabola that opens down, but it's not an even function.

To illustrate Mr. T's point:

Here is a screen shot, assuming the quiz is the same every time.

 

[gracy]

That's the equation of only a parabola that opens up and has its vertex at (0,0).

Could you please help me with upside down parabola equation?

 

[HallsofIvy]

In the "basic" parabola, $f(x)= x^2$, what is f(2)? In your graph, what is f(2)? What is the difference between the two?

 

[gracy]

what is f(2)?

4.

In your graph, what is f(2)?

-2.

What is the difference between the two?

4-(-2)=6

 

[HallsofIvy]

Then your basic problem is that you are reading your graph wrong. Looking at your graph I see f(2)= -4. Further f(1)= -1 and f(3/2) is about -9/4. Get the idea?

 

[gracy]

your graph

I want to make sure
Actually graph I am referring is the one in post #4 by Sammy s

 

[Mister T]

Could you please help me with upside down parabola equation?

$y=ax^2+bx+c$ is the equation of a parabola.

In the following discussion, what I mean by different conditions is different choices for the values of $a$, $b$, and $c$.

Under what conditions does the parabola open up versus open down. Under what conditions does the y-axis pass through the vertex?

Can this function ever be odd? Can it ever be even? Under what conditions?

I suggest you review the equation of a parabola in an elementary algebra textbook before tackling the more advanced notion of odd and even functions. You will make far better progress that way than in a forum conversation. When you are reviewing the concept in a textbook and get stuck on something ask here. That's when a forum conversation can be more helpful.

 

[Ray Vickson]

<[/PLAIN] Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

http://www.chilimath.com/flash-quiz/algebra/intermediate/oef/odd-even-functions-quiz.html
In this quiz I got all correct except 4th question.
I know how to figure out function is odd or even but for that I have to know the function of the graph I know equation of parabola is $f(x)$=$x^2$
but I don't know whether it is applicable for upside down parabola,by upside down parabola I mean parabola of this type

The definition of even or odd (or neither) has absolutely nothing at all to do with whether the graph is an upward-opening parabola or a downward-opening parabola, or whether it is a parabola at all! You claim to know how to figure out whether the function is even or odd. Well, show us how you would do that---and please don't tell us that you need to know how the parabola opens up. If you think you need to know that, then you really do not know the material. That, at least, would give us a starting point for further discussion.

 

[krebs]

Even function: mirrored on y-axis http://tube.geogebra.org/m/1963927
Odd function: mirrored on the origin http://tube.geogebra.org/m/X9hdpoXV
Otherwise it is neither.

 

[gracy]

I don't understand how this works.

 

[krebs]

I don't understand how this works.

What do you not understand?

Here's another example of what an "odd" function will look like. If you rotate the right side 180 degrees around the origin, you get the left side of the curve. That is why it is called "odd". rotating it 180 degrees is the same as flipping it on the x and y axis, or mirroring it across the origin. http://tube.geogebra.org/m/1964099

 

[krebs]

Here's the same as above, except the graph is moved up 1 unit on the y axis. Now if we rotate the right side around the point (0,0), it doesn't match up with the left side, so it's not odd anymore.http://tube.geogebra.org/m/1964117

 

[SammyS]

I don't understand how this works.

gracy,

You need to be much more specific regarding what you refer to.

 

[Mark44]

I don't understand how this works.

gracy,

You need to be much more specific regarding what you refer to.

I agree completely. @gracy, please don't waste our time this way. "I don't understand how this works." is not a question. We also have no way of knowing what you're referring to with "this" -- there were posts by three other members that preceded your comment. If you have a question about something that someone wrote, use the Quote button to highlight it so that we know what you're talking about.

 

[gracy]

use the Quote button

I always do,this time I forgot.