Algebra

Question

find a real-life application of each graph. Relate the application to the specific graph (line, parabola, hyperbola, exponential). Describe the characteristics of each application as related to the graph.

Answer

<P>Dear Natali,<BR><BR>We have seen this question at least twice in the past few weeks, once asked by Krista on June 9 and then by Tina on July 10.&nbsp; Are they classmates of yours, perhaps?<BR><BR>I thought I had seen it at least one other time but I cannot find it in the archives.&nbsp;&nbsp;<BR>&nbsp;&nbsp;<BR>You probably realize that a line is of the form y = ax +b<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; parabola is of the form y = ax^2 +&nbsp;c<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; exponential is of the form y =&nbsp;a*exp(bx) + c<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; hyperbola is of the form&nbsp;(x/a)^2 - (y/b)^2 = c^2<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;consequently,<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y/b = +/- sqrt((x/a)^2-c^2)<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; y = +/- b*sqrt((x/a)^2-c^2)<BR><BR>A&nbsp;hyperbola can also&nbsp;be described by&nbsp;c = xy.<BR><BR>I don't know what else you're studying in school besides math -- but you ought to be able to find some examples.&nbsp;&nbsp;<BR><BR>Right off the top of my head, I'm thinking&nbsp;physics.<BR><BR>Take&nbsp;Newton's equations, for instance.&nbsp;&nbsp;<BR><BR>F&nbsp;= ma.&nbsp;&nbsp;For&nbsp;a constant force, you could set up an&nbsp;experiment.&nbsp; Take&nbsp;items of several different masses and measure their&nbsp;acceleration.&nbsp; Maybe&nbsp;you could pull&nbsp;back a spring a set distance, and then&nbsp;plot mass and&nbsp;acceleration on the same graph.&nbsp; (You will see only the positive side of the hyperbola though).<BR><BR>Then, you could try constant mass and varying force, and plot force against acceleration.&nbsp; <BR><BR>While you're fooling around with that spring, you could test out Hooke's law.&nbsp; See if the energy in that spring really is proportional to the square of the distance that you pull it back.&nbsp;&nbsp;&nbsp;&nbsp;<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<BR>Exponential - interest compounded continuously is an exponential function.&nbsp;Set up an interest-bearing&nbsp;bank account with&nbsp;interest compounded continuously (make just one large deposit at the beginning),&nbsp;and then look at&nbsp;your&nbsp;balance over time.&nbsp;<BR><BR><BR>&nbsp; </P> http://vrd.askvrd.org/services/answerschema.xml