How to determine algebraically if the vertex of a quadratic equation is inside a 2D triangle?

Question

The quadratic equation is $y=x^2-2x+C$.

The triangle`s coordinates are for example, $(0,0)$ $(3,0)$ $(3,4)$. How do a I find the interval for the values of C for which the vertex of the quadratic equation is inside or outside the triangle?

The method proposed by @prakash chandel works if only one point is to be calculated.

Answer 1

Hint: compute the area of $\Delta$ ABC.let new point is X has cordinate ($x_{1}$,$x_{2}$). compute the area of $\Delta$XBC,$\Delta$XAC,and $\Delta$XBA .if $\Delta$ABC=$\Delta$XBC+$\Delta$XBA+$\Delta$XAC then points lie inside or on the the triangle otherwise outside.