Answered

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

Verified Answer :

nobillionaireNobley

While the vertex of the function f(x) = x^2 is (0, 0), the vertex of the function g(x) = x^2 + 2x + 1 is (-1, 0).
Whereas both function has same y-cordinate, their x-coordinate are different which indicates that the function g(x) = x^2 + 2x + 1 is a horizontal translation of the function f(x) = x^2.

calculista

we know that

The vertex of the function

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

is the point \((0,0)\)

and

the function

\(g(x)=x^{2} +2x+1\)

is equal to

\(g(x)=(x+1)^{2}\)

so

the vertex is the point \((-1,0)\)

therefore

the answer is

The translation to maps the vertex of f(x) onto the vertex of g(x) has the following rule

\((x,y)--------> (x-1, y)\)

check

\((0,0)----> (0-1,0)----> (-1,0)\) is ok

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