Question

1. Give an example of a quadtratic whose recirpocal has no vertical asymptotes

Ans. y = x^2 - 2x + 3

2. Compare the vertex (or turning point) of the quadratic and the corresponding feature of the reciprocal. Write down your observation.

What does the question mean by corresponding feature?

And what would be the observation be. I realised the x-coorindate remains the same.

Answer 1

your example would work.
As long as you pick a quadratic function which does not have any x-intercepts, that is , it does not cross the x-axis, it would work

That would mean that the corresponding equation f(x) = 0 would not have a solution in the real numbers

your resulting curve of the reciprocal would be a shallow bell curve whose maximum point has the same x coordinate as the vertex of the original function.
You could use something like
http://fooplot.com/
to see your two graphs

Answer 2

Ivé graphed the function, and would it be correct to say that if the vertex was (1,2), the corresponding feature's coordinates will be (1,1/2), the y coordinates will reciprocals of each other.

Answer 3

yes
Since you are basically taking 1/y for each y value, the height of the function would be the reciprocal of the original value

e.g.
if the height of the original was 5, then the corresponding height would be 1/5 or .2

if the height of the orignal is 1/10 then the new height wouldbe 10

etc.