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18 August, 19:41

Consider g (x) = - x^2 + 12x - 32 Part A: Write g (x) in vertex form, identify the vertex, and determine the x-intercepts.

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  1. 18 August, 20:12
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    (x - 6) ² = - (y - 4)

    The vertex of the parabola will be (6,4).

    The x-intercepts are at (8,0) and (4,0).

    Step-by-step explanation:

    Given the equation of parabola is g (x) = y = - x² + 12x - 32 ... (1)

    Now, converting the equation to vertex form.

    Here, y = - x² + 12x - 32

    ⇒ y = - (x² - 12x + 36) + 4

    ⇒ y - 4 = - (x - 6) ²

    ⇒ (x - 6) ² = - (y - 4) ... (2) (Answer)

    Now, the vertex of the parabola will be (6,4) and it opens down. (Answer)

    Let the x-intercept of the parabola is at (h, 0).

    Hence, from equation (2) we get,

    (h - 6) ² = - (0 - 4) = 4

    ⇒ h - 6 = ± 2

    ⇒ h = 8 or h = 4

    Therefore, the x-intercepts are at (8,0) and (4,0). (Answer)
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