The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. Which graph represents g(x)?

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11-01-2018
Mathematics

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The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. Which graph represents g(x)?

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MsEHolt MsEHolt · Answer 1 · 2018-06-10T02:53:20+02:00

The graph would be translated 5 units right and 1 unit up, giving an upward facing parabola with a vertex at (5, 1).

Explanation:
Since 5 was subtracted from x before it was squared, this means a horizontal translation 5 units. Since it was subtracted, this means it was translated right 5 units.

The 1 added at the end means it was translated 1 unit up as well.

This is in vertex form, y=a(x-h)^2 + k, where (h, k) is the vertex; h corresponds with 5 and k corresponds with 1, so the vertex is at (5, 1).

wagonbelleville wagonbelleville · Answer 2 · 2019-03-11T07:25:46+01:00

Answer:

Function f(x) is translated 5 units to the right and 1 unit upwards to get g(x) shown below.

Step-by-step explanation:

We are given that,

The function [tex]f(x)=x^2[/tex] is translated to form the function [tex]g(x)=(x-5)^2+1[/tex].

So, we see that,

The function f(x) is translated 5 units to the right which gives the function [tex](x-5)^2[/tex].

Further, this function is translated to 1 unit upwards which gives the function g(x).

That is, the function f(x) is translated 5 units to the right and 1 unit upwards to get g(x).

Thus, the graph of g(x) is shown below.