Select the graph that correctly represents ƒ(x) = –2(x + 4)2 – 1.Find the equation of the parabola with its focus at (3,4) and its directrix

Question

Select the graph that correctly represents ƒ(x) = –2(x + 4)2 – 1.Find the equation of the parabola with its focus at (3,4) and its directrix y = 0.

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King 4 years 2021-09-02T12:19:15+00:00 1 Answers 15 views 0

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  1. Sapo1
    0
    2021-09-02T12:21:00+00:00
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    Answer:

    Equation of parabola:  8*(y – 2) = (x – 3)^2

    or

    y = (1/8)*(x – 3)^2 + 2

    Step-by-step explanation:

    focus at (3,4) and its directrix y = 0.

    Focus equation:  (h, k + c) = (3, 4)

    Directrix equation  y =  k – c = 0

    so  h = 3,   k + c = 4,   k – c = 0

    Solve  the system :  k + c = 4 and k – c = 0

    add the equations together:     k + c + k – c = 4 + 0

    2k = 4

    k = 2

    so   k + c = 4,    2 + c = 4,   c = 2

    4c (y – k) = (x –  h)^2

    4*2 *(y – 2) = (x – 3)^2

    8*(y – 2) = (x – 3)^2

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )