what is the vertex of the absolute value function defined by f(x) = |x-2| -7

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what is the vertex of the absolute value function defined by f(x) = |x-2| -7

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Josie 2 weeks 2021-09-10T13:12:08+00:00 1 Answer 0

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    2021-09-10T13:13:58+00:00

    Answer:

    The vertex of the function f(x) is at (2,-7)

    Step-by-step explanation:

    The function is given to be f(x) = |x-2| -7

    Now, f(x) = x – 2 – 7 = x – 9 for, (x – 2) ≥ 0, ⇒ x ≥ 2 ………… (1)

    and f(x) = 2 – x – 7 = – x – 5 for, (x – 2) < 0, ⇒ x < 2 ………….. (2)

    Now, solving equation (1) and (2), we get, x – 9 = – x – 5

    ⇒ 2x = 4

    x = 2

    And hence, from equation (1) we get, y = x – 9 = 2 – 9 = – 7

    Therefore, the vertex of the function f(x) is at (2,-7) (Answer)

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