Answer:
[tex]f(x)=(x+1)^2[/tex]
Step-by-step explanation:
We have been given graph of a function. We are asked to find the equation of the graphed function.
Upon looking at our given graph, we can see that the graph represents a parabola.
We know that vertex form of a parabola is: [tex]y=a(x-h)^2+k[/tex], where, (h,k) represents the vertex of parabola.
We can see that vertex of our given parabola is at point [tex](-1,0)[/tex], so substituting the coordinates of vertex of parabola, we will get:
[tex]y=a(x--1)^2+0[/tex]
[tex]y=a(x+1)^2[/tex]
Now we will find the value of a using coordinates of point (0,1) in above equation.
[tex]1=a(0+1)^2[/tex]
[tex]1=a(1)^2[/tex]
[tex]1=a*1[/tex]
[tex]1=a[/tex]
Therefore, the equation of our graphed function would be [tex]f(x)=(x+1)^2[/tex]
