Question

The parametric equations x=t+1 and y=t^2+2t+3 represent the motion of an object. What is the shape of the graph of the equations? what is the direction of motion?

A. A parabola that opens upward with motion moving from the left to the right of the parabola.
B. A parabola that opens upward with motion moving from the right to the left of the parabola.
C. A vertical ellipse with motion moving counterclockwise.
D. A horizontal ellipse with motion moving clockwise.

Answer 1

A) A parabola that opens upward with motion moving from the left to the right of the parabola.

Explanation:

`x=t+1\rightarrow t=x-1\\\\y=t^2+2t+3\\y=(x-1)^2+2(x-1)+3\\y=x^2-2x+1+2x-2+3\\y=x^2+2`

Therefore, we can see that the shape of the graph is a parabola that opens upward with motion moving from the left to the right of the parabola.