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ale4655
1 month ago
5

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?

Mathematics
2 answers:
zzz [12.3K]1 month ago
8 0

we know that

The vertex of the function

f(x)=x^{2}

is indicated by the point (0,0)

and

the function

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

can be expressed as

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

so

the vertex is determined at the point (-1,0)

therefore

the response is

The translation that relocates the vertex of f(x) to that of g(x) is defined by the following rule

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

check

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

PIT_PIT [12.4K]1 month ago
4 0
While the vertex of the function f(x) = x^2 is at (0, 0), the vertex of the function g(x) = x^2 + 2x + 1 is at (-1, 0).
Although both functions share the same y-coordinate, the x-coordinates differ. This indicates that g(x) = x^2 + 2x + 1 represents a horizontal shift of f(x) = x^2.
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