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Verified Answer :

Edufirst

When you add a positive value to the argument of a function, its graph shifts to the left, the same number of units added to the argument.

This is, the graph of f(x+a) is the graph of the function f(x) shifted a units to the left.

Then, g(x) is f(x+3) = (x+3)^2

calculista

we have

\(f(x)=x^{2}\)

This is the equation of a vertical parabola open upward with the vertex at point \((0,0)\)

we know that

The graph of f(x) is is shifted \(3\) units to the left to obtain the graph of g(x)

so

The rule of the translation is

\((x,y)------> (x-3,y)\)

Applying the rule of the translation at the vertex of the graph of f(x)

\((0,0)------> (0-3,0)\)

\((0,0)------> (-3,0)\)

The vertex of the graph of g(x) is the point \((-3,0)\)

therefore

the answer is

The equation of g(x) is equal to

\(g(x)=(x+3)^{2}\)

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