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Numerade Educator

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Problem 23 Easy Difficulty

Match the parametric equations with the graphs (labeled I-VI). Give reasons for your choices.

$ x = t $ , $ y = \frac{1}{(1 + t^2)} $ , $ z = t^2 $

Answer

Graph 5

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Video Transcript

So what we're given is that X is equal to t. Why is equal to 1/1 plus t squared and Z is equal to t Square. So with this, we consider the given equations in the xz plane and we see that Z is going to equal X squared because we just plug in this value right here. So since because is X squared, that means that we have a projection that's a parabola. And then we also observe that the winds coordinates are never negative. Um, so we see that Y is going to be greater than or equal to zero, and Z is going to be greater than or equal to zero for all values of X. Um, so both of these properties are going to be only seen in graph five. So based on that, we can assume and predict and know that, given all of our options, these properties right here tell us that graph five is going to be the graph that's best described by these parametric equations