keeping in mind that we could have a horizontally opening parabola or a vertically opening one using those values, let's use the vertical parabola type for the equation
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(0,1)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]y=a(x-0)^2+1\implies y=ax^2+1\qquad \textit{we also know that when} \begin{cases} x = -1\\ y = 0 \end{cases} \\\\\\ 0 = a(-1)^2+1\implies 0=a+1\implies \boxed{-1=a} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-x^2+1\implies \stackrel{\textit{vertex form}}{y = -(x-0)^2+1}~\hfill[/tex]
