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Match the vector equations in Exercises $1 - 8$ with the graphs $( a ) - ( h )$ given here.

$$

\mathbf { r } ( t ) = \left( t ^ { 2 } - 1 \right) \mathbf { j } + 2 t \mathbf { k } , \quad - 1 \leq t \leq 1

$$

graph F

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University of Michigan - Ann Arbor

okay. Were given a vector equation. Are, uh, T is equal to, um t squared minus one. Um, j plus two tea. Kay whips. I went too far out there. Um, okay. And t goes from negative One toe, one inclusive. Okay. And we want to kind of pair it up with a crap. Let's go ahead and develop our own graph. Let's see if we can do this and then look at our options. Okay? So, Z, why is right there in the ex is coming out of the board. But I don't even have to worry about the x axis because Jay is the Y. Playing Kay is a seaplane, so I know I only have something in the Y, um Z playing. Okay, so if I start right off at Ti umm is zero, then my wife value is out here. Negative one. If I have a, um t of negative one. Um, I have nothing on the why. It's gonna be in my Z. So this will be down here at negative too. And the same thing with a positive one. I will be up here at Ah, positive, too. So I'm gonna start with negative one and go to positive, too, in that direction. And so if I look at my choices, this is gonna be choice F.

University of Central Arkansas