Question

A curve is described by the following parametric equations: x+3+t, y=t^2-4

Which statement best describes the curve?
1 The curve is a parabola with a vertex at left parenthesis 3 comma negative 4 right parenthesis and is traced from left to right for increasing values of t.
2 The curve is a parabola with a vertex at left parenthesis 3 comma negative 4 right parenthesis and is traced from right to left for increasing values of t.
3 The curve is a parabola with a vertex at left parenthesis negative 3 comma 4 right parenthesis and is traced from left to right for increasing values of t.
4 The curve is a parabola with a vertex at left parenthesis negative 3 comma 4 right parenthesis and is traced from right to left for increasing values of t.
2

Answer 1

The curve is a parabola with a vertex at left parenthesis 3 comma negative 4 right parenthesis and is traced from left to right for increasing values of t.

Step-by-step explanation

The given curve is defined parametrically as;

`x = 3+ t`

`y = {t}^(2) - 4`

We need to eliminate the parameter by making t the subject in the first equation and substitute into the second equation.

`t = x - 3`

`y = {(x - 3)}^(2) - 4`

This is a parabola that has its vertex at (3,-4).

This parabola opens upwards.