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23 April, 16:14

Which translation maps the vertex of the graph of the function f (x) = x2 onto the vertex of the function g (x) = - 8 + x^2 + 7?

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  1. 23 April, 18:27
    0
    The function translated 4 units right and 9 units down

    The third answer

    Step-by-step explanation:

    * To solve the problem you must know how to find the vertex

    of the quadratic function

    - In the quadratic function f (x) = ax² + bx + c, the vertex will

    be (h, k)

    - h = - b/2a and k = f (-b/2a)

    * in our problem

    ∵ f (x) = x²

    ∴ a = 1, b = 0, c = 0

    ∵ h = - b/2a

    ∴ h = 0/2 (1) = 0

    ∵ k = f (h)

    ∴ k = f (0) = (0) ² = 0

    * The vertex of f (x) is (0, 0)

    ∵ g (x) = - 8x + x² + 7 ⇒ arrange the terms

    ∴ g (x) = x² - 8x + 7

    ∵ a = 1, b = - 8, c = 7

    ∴ h = - (-8) / 2 (1) = 8/2 = 4

    ∵ k = g (h)

    ∴ k = g (4) = (4²) - 8 (4) + 7 = 16 - 32 + 7 = - 9

    ∴ The vertex of g (x) = (4, - 9)

    * the x-coordinate moves from 0 to 4

    ∴ The function translated 4 units to the right

    * The y-coordinate moves from 0 to - 9

    ∴ The function translated 9 units down

    * The function translated 4 units right and 9 units down
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