Draw the parabola.

Find the point of intersection.

So i was trying to do this question. My teacher told me that whenever you see f(x) = 1/x then assume that it's the reciprocal function and the graph always takes the same shape...here'z the link for the shape:-

http://www.gomath.com/htdocs/images/7-10...
so shouldn't the equation y=1/2x^2 - 3 take the same shape... isn't it the reciprocal function because when i graph it on a graphing calculator it takes the shape of a parabola and i checked the answer the teacher gave us, and he also made it in a shape of parabola... can some1 explain me how do i come to know when is it reciprocal function and when is it a parabola

Plz help me asap.. i have a test on this tomorrow... thnx

(i don't know calculus)