Consider the following equations. x = 1 − t2, y = t − 5, −2 ≤ t ≤ 2 (a) Sketch the curve by using the parametric equations to pl
ot points. Indicate with an arrow the direction in which the curve is traced as t increases.
2 answers:
Answer:
A parable opened to the left!
Step-by-step explanation:
<h2>Easy, easy! </h2><h2>Well, if you can draw!!!</h2><h2 /><h3>First, the parameter is t!</h3><h3>So for each value of t, there is a value for x and y!</h3><h3>That is if t=-2, x=-3 and y=-7 because x=1-(2)^2= 1-4=-3, and y=(-2)-5=-7.</h3><h3 /><h3>Then we take the next values for t and get x and y</h3>t= -2, -1, 0, 1, 2
x= -3, 0, 1, 0, -3
y= -7, -6, -5, -4, -3,
As you can see in the graphics, there are many other point in order to get a very clear view. The result is parable that opens its arms to the left starting from the bottom left, at the point (-3,-7) at t=-2, then goes to the upright until the point (1,-5), at t=0, then goes back to the left keeping upward until the point (-3,-3), at t=2.
Answer:
See graph attached.
The path of the curve, as t increases goes from the top of the curve going down, following a parabola symmetric in y=5.
Step-by-step explanation:
We have the following parametrics equations:
We can graph the variables x and y in a xy-plane following the values of t within the interval defined.
To do that we compute the values for x and y for every t in the interval and graph it.
The path of the curve, as t increases goes from the top of the curve going down, following a parabola symmetric in y=5.
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The inverse of this function is y = x -
You can find the inverse of any function by switching the x and y values and then solving for the new y value. Once you've done that, what will be left over is the inverse function.
y = ----> Swap x and y
x = -----> Subtract 3/4 from both sides.
x - = y ----> rearrange to appropriate order
y = x -
And that is your inverse function.