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12 July, 15:58

Find the x-intercepts of the parabola with vertex (6,27) and y-intercept (0,-81). write answer in form (x1, y1) (x2, y2). if necessary, round to the nearest hundredth.

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  1. 12 July, 16:25
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    The vertex form of the equation is:

    y = a (x - h) ² + k

    - 81 = a (0 - 6) ² + 27

    - 81 = 36 a + 27

    - 108 = 36 a

    a = - 108 : 36

    a = - 3

    y = - 3 (x - 6) ² + 27

    y = - 3 (x² - 12 x + 36) + 27

    y = - 3 x² + 36 x - 108 + 27

    y = - 3 x² + 36 x - 81

    y = - 3 (x² - 12 x + 27)

    x² - 12 x + 27 = 0

    x² - 9 x - 3 x + 27 = 0

    x (x - 9) - 3 (x - 9) = 0

    (x - 9) (x - 3) = 0

    x 1 = 3, x 2 = 9

    Answer:

    The x-intercepts are (3, 0) and (9, 0).
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