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1 day ago

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 [9K]1 day 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

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

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 [9.1K]1 day 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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