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Which statements describe one of the transformations performed on ๐‘“(๐‘ฅ)=๐‘ฅ2f(x)=x 2 to create ๐‘”(๐‘ฅ)=(๐‘ฅโˆ’2)2+5g(x)=(xโˆ’2) 2 +5? Choose all that apply.A.A translation of 5 units upB.A translation of 2 units to the leftC.A translation of 2 units to the rightD.A translation of 5 units downSUBMITarrow_backPREVIOUS

Question

Which statements describe one of the transformations performed on ๐‘“(๐‘ฅ)=๐‘ฅ2f(x)=x 2 to create ๐‘”(๐‘ฅ)=(๐‘ฅโˆ’2)2+5g(x)=(xโˆ’2) 2 +5? Choose all that apply.A.A translation of 5 units upB.A translation of 2 units to the leftC.A translation of 2 units to the rightD.A translation of 5 units downSUBMITarrow_backPREVIOUS

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Solution

The transformations performed on ๐‘“(๐‘ฅ)=๐‘ฅ^2 to create ๐‘”(๐‘ฅ)=(๐‘ฅโˆ’2)^2+5 are:

A. A translation of 5 units up B. A translation of 2 units to the right

Explanation:

The general form of a quadratic function is f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

In the function ๐‘”(๐‘ฅ)=(๐‘ฅโˆ’2)^2+5, the vertex is (2,5).

Compared to the original function ๐‘“(๐‘ฅ)=๐‘ฅ^2, which has a vertex at (0,0), we can see that the function has been shifted 2 units to the right and 5 units up.

Therefore, the correct answers are A and B.

This problem has been solved

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