Answer
(a) We can see the graph below.
(b) $y = x-6$, where $x \geq 2$
Work Step by Step
$x = t^2+2$
$y = t^2-4$
(a)
t = -2:
$x = (-2)^2+2 = 6$
$y = (-2)^2-4 = 0$
t = -1:
$x = (-1)^2+2 = 3$
$y = (-1)^2-4 = -3$
t = 0:
$x = (0)^2+2 = 2$
$y = (0)^2-4 = -4$
t = 1:
$x = (1)^2+2 = 3$
$y = (1)^2-4 = -3$
t = 2:
$x = (2)^2+2 = 6$
$y = (2)^2-4 = 0$
(Note that $x \geq 2$)
We can see the graph below.
(b)
$x = t^2+2$
$t = \sqrt{x-2}$
$y = t^2-4$
$y = (\sqrt{x-2})^2-4$
$y = (x-2) - 4$
$y = x-6$
(Note that $x \geq 2$)
