Answer:
[tex]y=(x-1)^{2}-3[/tex]
Step-by-step explanation:
According to the graph, the vertex of the parabola is at (1,-3), which means h = 1 and k = -3
Also, the parabola has y-intercept at (0,-2).
Using this information and the form [tex]y=a(x-h)^{2} +k[/tex], we can find the equation. First, we need to find [tex]a[/tex]
[tex]y=a(x-h)^{2} +k\\-2=a(0-1)^{2}-3\\-2+3=a\\a=1[/tex]
Therefore, the equation is
[tex]y=(x-1)^{2}-3[/tex]
(The image attached shows the graph of our function, notice that it's the same)