The vertex form of a parabola is:
[tex]y=a(x-h)^2+k[/tex]
where (h,k) is the vertex and a is some constant.
From the graph, the vertex is located at (-2, 2), that is, h = -2 and k = 2. Substituting into the equation, we get:
[tex]\begin{gathered} y=a(x-(-2))^2+2 \\ y=a(x+2)^2+2 \end{gathered}[/tex]
Also, the point (-1, 5) is on the parabola, then:
[tex]\begin{gathered} 5=a(-1+2)^2+2 \\ 5=a\cdot1+2 \\ 5-2=a \\ 3=a \end{gathered}[/tex]
Finally, the equation is:
[tex]y=3(x+2)^2+2[/tex]
