A curve is describe by the following parametric equations:

x=3+t, y=t^2-4

Which statement best describes the curve?

A. The curve is a parabola with a vertex at (3,-4) and is traced from left to right for increasing values of t.

B. The curve is a parabola with a vertex at (3,-4) and is traced from right to left for increasing values of t.

C. The curve is a parabola with a vertex at (-3,4) and is traced from left to right for increasing values of t.

D. The curve is a parabola with a vertex at (-3,4) and is traced from right to left for increasing values of t.

Question

Maritza Johnston

Mathematics

30 November, 16:52

A curve is describe by the following parametric equations:

x=3+t, y=t^2-4

Which statement best describes the curve?

A. The curve is a parabola with a vertex at (3,-4) and is traced from left to right for increasing values of t.

B. The curve is a parabola with a vertex at (3,-4) and is traced from right to left for increasing values of t.

C. The curve is a parabola with a vertex at (-3,4) and is traced from left to right for increasing values of t.

D. The curve is a parabola with a vertex at (-3,4) and is traced from right to left for increasing values of t.

+4

Answers (1)

Know the Answer?

Alani Kemp · Answer 1

A. The curve is a parabola with a vertex at (3,-4) and is traced from left to right for increasing values of t.

Step-by-step explanation:

x = 3 + t

y = t² - 4

Eliminating the parameter:

t = x - 3

y = (x - 3) ² - 4

This is an upwards parabola with a vertex at (3, - 4).

x = 3 + t, so as t increases, x increases.

So the curve is traced from left to right.