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20 December, 06:31

The equation of a parabola is given.

y=1/2x^2+6x+24

What is the equation of the directrix of the parabola?

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Answers (1)
  1. 20 December, 09:30
    0
    Directrix equation: y = 11/2

    y = k - c = 6 - 1/2 = 11/2

    Step-by-step explanation:

    y = (1/2) x^2+6x+24

    factor this

    y = (1/2) * [ x^2 + 12x ] + 24

    y = (1/2) * [ x^2 + 12x + 36 - 36] + 24

    y = (1/2) * [ (x + 6) ^2 - 36] + 24

    y = (1/2) * (x + 6) ^2 - 18 + 24

    y = (1/2) * (x + 6) ^2 + 6

    y - 6 = (1/2) * (x + 6) ^2

    2 * (y - 6) = (x + 6) ^2

    4c = 2, (h, k) = (-6, 6)

    c = 1/2

    Directrix equation: y = k - c = 6 - 1/2 = 11/2
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