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

ANSWER

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.

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.