Write an equation in vertex form of the parabola that passes through (4, 20) and has a vertex of (1, 2). *

Question

Write an equation in vertex form of the parabola that passes through (4, 20) and has a vertex of (1, 2). *

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Bella 1 week 2022-01-10T23:47:20+00:00 1 Answer 0 views 0

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    2022-01-10T23:49:03+00:00

    Answer:

    f(x) = 2(x – 1)² + 2

    Step-by-step explanation:

    The vertex form is f(x) = a(x – h)² + k, where the vertex is (h, k).

    Putting in the given vertex, we get  f(x) = a(x – 1)² + 2. To find a, we put in the other point that the parabola passes through (4, 20) which is [x, f(x)].

    20 = a(4 – 1)² + 2

    20 = a(3)²  +  2

    20 = 9a + 2    (subtract 2 from both sides to get a alone)

    -2            -2

    18  =  9a    (divide both sides by 9 to get a by itself)

    9       9

    2 = a   (put that into our vertex form equation)

    f(x) = 2(x – 1)² + 2

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