Answer:
[tex]y=x^2-4[/tex]
Step-by-step explanation:
we know that
The function of the graph is a vertical parabola open upward
The vertex is a minimum
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem
Looking at the graph
The vertex is the point (0,-4)
substitute
[tex]y=a(x-0)^2-4[/tex]
[tex]y=ax^2-4[/tex]
To determine the value of "a" take a point in the graph
I take the point (3,5)
substitute the value of x and the value of y and solve for a
[tex]5=a(3)^2-4\\9a=5+4\\9a=9\\a=1[/tex]
therefore
The equation of the quadratic function is
[tex]y=x^2-4[/tex]
