Chapter 6.3, Problem 17E

Solution

To eliminate: The parameter and identify the graph. Use the graph to support your answer.

The general equation is $y=x^3-2x+3$ and the graph is shown in figure $\left(1\right)$ .

Given information:

The equations are $x=t$ and $y=t^3-2t+3$ .

Calculation:

Substitute the $x$ for $t$ to the equation $y=t^3-2t+3$ .

  $y=x^3-2x+3$

This is a cubic polynomial (3rd degree polynomial). This is supported by the graph obtained from the parametric equations as there are three intercepts.

  

Figure (1)

Therefore, the general equation is $y=x^3-2x+3$ and the graph is shown in figure $\left(1\right)$ .