Answer:
[tex]y=2x^{2}+1[/tex]
Step-by-step explanation:
we know that
The graph is a vertical parabola open upward
The vertex is the point (0,1)
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
substitute the vertex in the equation
[tex]y=a(x-0)^{2}+1[/tex]
[tex]y=a(x)^{2}+1[/tex]
Find the value of coefficient a
Observing the graph
For x=1, y=3
substitute in the equation
[tex]3=a(1)^{2}+1[/tex]
[tex]a=3-1=2[/tex]
The equation on the graph is equal to
[tex]y=2x^{2}+1[/tex]
