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11 June, 10:16

What is the vertex form of the parabola whose standard form equation is y=5x^2-30x+49

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  1. 11 June, 10:30
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    The vertex is (3,4)

    Step-by-step explanation:

    To convert a quadratic from

    y = a x 2 + b x + c

    form to vertex form,

    y = a (x - h) 2 + k, you use the process of completing the square.

    First, we must isolate the x

    terms:

    y - 49 = 5 x 2 - 30 x + 49 - 49

    y - 49 = 5 x 2 - 30 x

    We need a leading coefficient of 1

    for completing the square, so factor out the current leading coefficient of 2.

    y - 49 = 5 (x 2 - 6 x)

    Next, we need to add the correct number to both sides of the equation to create a perfect square. However, because the number will be placed inside the parenthesis on the right side we must factor it by

    2

    on the left side of the equation. This is the coefficient we factored out in the previous step.

    y - 49 + (5 ⋅?) = 5 (x 2 - 6 x + ?)

    < - Hint:

    62 = 3; 3 ⋅ 3 = 9

    y - 49 + (5 ⋅ 9) = 5 (x 2 - 6 x + 9)

    y - 49 + 45 = 5 (x 2 - 6 x + 9)

    y - 4 = 5 (x 2 - 6 x + 9)

    Then, we need to create the square on the right hand side of the equation:

    y - 4 = 5 (x - 3) 2

    Now, isolate the y term:

    y - 4 + 4 = 5 (x - 3) 2 + 4

    y - 0 = 5 (x - 3) 2 + 4

    y - 0 = 5 (x - 3) 2 + 4

    The vertex is:

    (3, 4)
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