Working with parametric equations Consider the following parametric equations.

a. Make a brief table of values of t, x, and y.

b. Plot the points in the table and the full parametric curve, indicating the positive orientation (the direction of increasing t).

c. Eliminate the parameter to obtain an expiation in x and y.

d. Describe the curve.

x = t2+ 2, y = 4t; −4 ≤ t ≤ 4

Solution 8E

Step 1:

Table of the values of t, x and y:

-4 |
18 |
-16 |

-3 |
11 |
-12 |

-2 |
6 |
-8 |

-1 |
3 |
-4 |

0 |
2 |
0 |

1 |
3 |
4 |

2 |
6 |
8 |

3 |
11 |
12 |

4 |
18 |
16 |

Step 2:

Plot of the points in the table and indication of positive orientation: