The vertex form of a parabola is:
[tex]y=a(x-h)^2+k[/tex]
where (h, k) is the vertex of the parabola and a is some constant.
From the graph, the vertex is located at (1, 4), that is, h = 1 and k = 4.
Substituting with these values and the point (0, 3), we get:
[tex]\begin{gathered} 3=a(0-1)^2+4 \\ 3-4=a(-1)^2 \\ -1=a\cdot1 \\ -\frac{1}{1}=a \\ -1=a \end{gathered}[/tex]
Then, the equation of the function is:
[tex]\begin{gathered} y=-1(x-1)^2+4 \\ y=-(x-1)^2+4 \end{gathered}[/tex]
