Answer
(a) We can see the graph below.
(b) $y = x-6$, where $x \geq 2$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/cf8a3c1f-9a64-4cec-920c-e99c5902bb04/result_image/1529587715.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000100Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=22ce3a2337f18c17625f598451d5dc3c63dde3fe18606851f9a619580197e89c)
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 $x \geq 2$)
![](https://gradesaver.s3.amazonaws.com/uploads/solution/cf8a3c1f-9a64-4cec-920c-e99c5902bb04/steps_image/small_1529587715.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000100Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=a7cd7995006617fe115ecb4e12df071197a3f73d3406bd5ef86622ef05d0847d)