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The equation for the red graph is f(x)=-x^2.
The question is an incomplete graph of a function is missing
For a complete question refer to the graph attached below
we have [tex]g(x)=4-x^2[/tex]
The vertex of the function g(x) is the point (0,4)
The vertex of the function f(x) is the point (0,0)
This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.
So, the rule of the translation of g(x) to f(x) is
(x,y)------> (x,y-4)
The translation is 4 units down
The equation of the function f(x) is
[tex]f(x)=g(x)-4[/tex]
[tex]f(x)=(4-x^2)-4[/tex]
[tex]f(x)=-x^2[/tex]
Therefore, The answer is f(x)=-x^2
To learn more about the graph visit:
https://brainly.com/question/4025726
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