Functions f(x) and g(x) are shown below: f(x) = x2 g(x) = x2 − 8x + 16 In which direction and by how many uni

Question

Functions f(x) and g(x) are shown below:

f(x) = x2
g(x) = x2 − 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)?

Left by 4 units

Right by 4 units

Left by 8 units

Right by 8 units

in progress 0
Margaret 17 hours 2021-11-25T11:44:15+00:00 2 Answers 0

Answers ( )

    0
    2021-11-25T11:45:36+00:00

    Answer:

    B, Right by 4 units

    Step-by-step explanation:

    we want to factor g(x), and the factorization of that would be (x – 4)² as its a perfect square trinomial

    when translating on a graph, we determine the translation. the translation of g(x) is a horizontal shift 4 units to the right, as we are subtracting 4. if it was adding 4, we would be shifting to the left 4 units

    0
    2021-11-25T11:46:05+00:00

    ANSWER

    Right by 4 units

    EXPLANATION

    The given functions are

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

    and

    g(x) =  {x}^{2}  - 8x + 16

    To obtain how much f(x) is shifted to obtain g(x), we need to rewrite g(x) in vertex form.

    Observe that,

    g(x) =  {x}^{2}  - 8x + ( - 4) ^{2}

    is a perfect square trinomial.

    The vertex form is

    g(x) =  {(x - 4)}^{2}

    When f(x) is shifted 4 units to the right, we obtain g(x).

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