Answer:
[tex]y = {x}^{2} - 2[/tex]
Step-by-step explanation:
Find a Rule means write a function for the graph. The graph is shaped like a U so the graph will be a quadratic, so the graph must have a term
[tex] {x}^{2} [/tex]
in it. We are given the vertex of the function. We can use vertex formula
[tex]y = (x - h) {}^{2} + k[/tex]
where h is the x value of the vertex and k is the y value of the vertex.
[tex]y = (x - 0) {}^{2} - 2[/tex]
[tex] y = {x}^{2} - 2[/tex]
So the rule is
[tex] {x}^{2} - 2[/tex]
