$\displaystyle y_0=a(-h)^2+b(-h)+c$
You can also get $\displaystyle y_1$ and $\displaystyle y_2$ in the same way.
Substitute expressions in terms of a,b,c and h for $\displaystyle y_0$,$\displaystyle y_1$ and $\displaystyle y_2$ into the second area formula and you will get the first area formula.