y = 2t..., when t = 0, y = 2 * 0 = 0.
y = 2t, if t > 0, y > 0 because t is positive and 2 is positive, +ve * +ve = +ve which is > 0.
That's simple, you can just sub in any values of t > 0 into y and see the trend: y > 0.
Read the explanation above and if you don't understand it, try it for t < 0, where x = t^2 - 2. You will see all your values tend to -2 or go further away from it. The smaller t is the further away it is from -2 (it is larger than it) and the greater it is when it is negative so e.g. -4, -3, -2, -1 ... (or closer to 0) the closer it is to -2, but it will never reach -2 except t = 0. So, you will be able to conclude: when t < 0, x > -2.
Brings £1m claim because he didn't get a first