A curve is described by the following parametric equations:
x = 2 - t
y = x^2 + 1
Which statement best describes the curve?

The curve is a parabola with a vertex at (2, 1) and is traced from left to right for increasing values of t.
The curve is a parabola with a vertex at (2, 1) and is traced from right to left for increasing values of t.
The curve is a parabola with a vertex at (-2, -1) and is traced from left to right for increasing values of t.
The curve is a parabola with a vertex at (-2, -1) and is traced from right to left for increasing values of t.

When you use a parameter to describe equations then you are talking about Parametric Equations, that is, you can write both [tex]x[/tex] and [tex]y[/tex] as functions of a parameter [tex]t[/tex]. In this problem we have the following equations:

[tex]x=2-t \\ y=x^{2}+1[/tex]

So substituting [tex]x[/tex] in [tex]y[/tex] we have:

[tex]y=(2-t)^2+1 \\ y=4-4t+t^2+1 \\ y=t^2-4t+5[/tex]

So this equation represents a parabola where [tex]y[/tex] is the dependent variable and [tex]t[/tex] is the independent variable. This equation is shown in the figure below, the best statement that describes this curve is:

The curve is a parabola with a vertex at (2,1) and is traced from left to right for increasing values of t.

swapnalimalwadeVT swapnalimalwadeVT · Answer 2 · 2022-04-20T07:05:46+02:00

A curve is described by parametric equations x = 2 - t;

y = x^2 + 1 statement the curve is a parabola with a vertex at (2,1) and is traced from left to right for increasing values of t is the best-described curve.

We use a parameter to describe equations then we are talking about Parametric Equations, that isWe can write both as functions of a parameter.

We have given the parametric equation

[tex]x = 2 - t\\y = x^2 + 1[/tex]

What is the parametric equation?

The parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

So substituting the value of x in y we get,

[tex]y=(2-t)^2+1\\y=2^2-4t+t^2+1\\y=4-4t+t^2+1\\y=5-4t+t^2\\[/tex]

So this equation represents a parabola where y is the dependent variable and t is the independent variable.

This equation is shown in the following figure, the best statement that describes the curve.

Therefore we can say that the curve is a parabola with a vertex at (2,1) and is traced from left to right for increasing values of t.

To learn more about the parametric equation visit:

https://brainly.com/question/51019