I have trouble grasping parabolas, and mainly the cartesian equations describing the,. In my mind, there are 4 possible parabolas, a parabola shaped like a mountain ($\cap$), a parabola shaped like a valley ($\cup$), a parabola shaped like the greater than sign ($\supset$) and a parabola shaped like the smaller than sign ($\subset$), of course without the sharp edges like they have in my examples. I know one standard equation:
$y-b = \dfrac{1}{4c}(x-a)^2$, with the vertex at $T(a,b)$ and the focus $F(a; b+c)$.
However, I don't know for which of the 4 this one is, so my questions are:
1. What is the equation of the $\cap$ shaped parabola?
2. What is the equation of the $\cup$ shaped parabola?
3. What is the equation of the $\subset$ shaped parabola?
4. What is the equation of the $\supset$ shaped parabola?
To clarify: I would like them in the same form as the one I noted above in the example, thanks in advance.