The given graph is a parabola.
We get the points (0,0) and (2,4) from the graph by observing the graph.
Here (0,0) is vertex.
Consider the equation of the parabola.
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex.
Substitute h=0, k=0 in the parabola equation, we get
[tex]y=a(x-0)^2+0[/tex][tex]y=ax^2[/tex]Substitute x=2 and y=4 to find the value of a.
[tex](4)=a(2)^2[/tex][tex]4=4a[/tex][tex]a=1[/tex]Substitute a=1 in the equation, we get
The equation of the given graph is
[tex]y=x^2[/tex]We know that the power function can be written as follows.
[tex]y=x^n[/tex]Compared with the given graph function, we get n=2.
Hence the given graph is a power function when n is even.
