SOLUTION: could someone please tell me the answer to this question? a parabola that opens to the right is a radicand,function,linear equation,or relation.thanks hagd.

Algebra.Com
Question 208012: could someone please tell me the answer to this question?
a parabola that opens to the right is a
radicand,function,linear equation,or relation.thanks
hagd.

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
a parabola that opens to the right is a relation.
-----
an equation is a function if there is one and only one value of y for each x.
otherwise it is a relation.
when you take a parabola and turn it to the right you get 2 values of y for each x which makes it not a function which makes it a relation.
-----
it is not a linear equation because a linear equation is an equation of a straight line.
-----
it might be a radicand but we'll have to see how that pans out.
a radicand is an expression under the root sign.
if you take the square root of x, then x is the radicand because it is under the square root sign.
-----
let's see what happens.
-----
a quadratic equation is an equation of a parabola.
let's take y = x^2 + 3x + 2
graph of this equation would be:

this is a parabola that opens upward.
it is a function because there is one and only 1 value of y for each x.
it is not a radicand because the equations is not under the root sign.
it is not a relation because it is a function. those are mutually exclusive.
it is not a linear equation because it is not the equation of a straight line.
-----
now let's take y = +/-
we got this equation by taking the previous quadratic equation of y = x^2 + 3x + 2 and solving for x and then making y = x and x = y.
graph of this equation would be:

this is a parabola that opens to the right.
it is not a function because there is more than 1 value of y for at least one of the x's.
it is a relation because it is not a function. those are mutually exclusive. the equation is either a function or a relation, never both.
it is not a linear eqution because it is not the equation of a straight line.
it is not a radicand because the whole equation is not under the radical sign, only a portion of it.
-----
interesting tidbit:
-----
the equation of y = +/- is the inverse equation of y = x^2 + 3x + 2.
you create an inverse equation by solving for x and then inverting the x and the y which is what we did.
this means that the equations are reflections of each other about the line y = x.
you should be able to see this in the following graph of both equations and the line y = x

-----
you probably didn't need to know that but since i created your right facing parabola by inverting your upward facing parabola, i thought you might be interested in the relationship that was created by doing that.
----
fyi,
the original equation is a function but the inverse equation is a relation because of the rules of functions described earlier. this is not always the case. it is just the case for this equation.
-----

RELATED QUESTIONS

Could someone please tell me if my answer is correct? I have 13.9% Question is The... (answered by Alan3354)
please help.I posted these about 3 days ago,but haven't got a response.Can someone... (answered by stanbon)
explain how you can tell whether a parabola opens upward, downward, to the left, or to... (answered by stanbon)
How can you tell if a parabola opens left/right or up/down such as for this question.... (answered by stanbon)
I was wondering if someone could please help me answer this question. The question is as... (answered by solver91311)
can someone tell me how to answer this question? please A student claims that the... (answered by stanbon)
I have a question that I think I know the answer to but I need someone to look it over... (answered by sabanasir)
I have tried to do this question a a lot of time but My answer and the Graph is not... (answered by ankor@dixie-net.com)
Ok. so this one is a graph of a positive, even parabola which means it opens up. the... (answered by scott8148)