Finding the parameter values of parametrized curve

Question

I'm kinda confused on how to find the values that a parameter takes given two points of parametrized curve, this is the problem I have:

Parametrize $y=x^2$ in the interval of the two points $(-1,1)$ and $(1,1)$ find the values of the parameter where this function takes value.

My solution was this, the parametrizatition is $x=t$ and $y=t^2$, this results in the fuction $\alpha =t \hat i+t^2 \hat j$, but I don't know what are the values of $t$ in the interval $(-1,1)\cup(1,1)$ for the parametrized curve.

Any help would be awesome, thanks.

Answer 1

I'm not sure whether you are very confused or if you are just using poor notation. You talk about $(-1, 1)\cup (1, 1)$ as if (-1, 1) and (1, 1) were intervals but you had already said that (-1, 1) and (1, 1) are points, not intervals! You have x= t so the values for t are just the values for x, -1 to 1.

Answer 2

You can choose an arbitrarily small step say 0.1

$$ x= \pm(.1,.2..3,.4,.5,.. 0.8,0.9,1)$$ $$ y= +(.01,.04,.09,.16,.25, ... 0.64,0.81, 1.0) $$