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 ->  Quadratic-relations-and-conic-sections -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
a parabola that opens to the right is a relation.
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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.
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it is not a linear equation because a linear equation is an equation of a straight line.
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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.
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let's see what happens.
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a quadratic equation is an equation of a parabola.
let's take y = x^2 + 3x + 2
graph of this equation would be:
graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+3x+%2B+2%29
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.
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now let's take y = +/- sqrt%28%28x+%2B+.25%29%29+-+1.5%29
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.
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interesting tidbit:
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the equation of y = +/- sqrt%28%28x+%2B+.25%29%29+-+1.5%29 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

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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.
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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.
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