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15 August, 15:55

Can someone explain to me how to find the vertex form of this equation?

y = - x^2 + 12x-4

Do i use the - b/2a formula? I just need this to be explained better biased on a equation i need to solve.

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  1. 15 August, 17:13
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    The quadratic equation has the general formula:

    y = ax^2 + bx + c

    The vertex form has the general formula:

    y = a (x-h) ^2 + k

    To get the vertex formula, we will need to get the values of a, h and k as follows:

    1 - The value of a:

    The value of "a" in the vertex form is the same as the value of "a" in the quadratic form

    Therefore: a = - 1

    2 - The value of h:

    the value of "h" can be computed using the formula:

    h = - b / 2a

    From the given quadratic equation: b = 12 and a = - 1

    Therefore: h = - 12 / 2 (-1) = 12/2 = 6

    3 - The value of k:

    The value of k can be computed easily by evaluating y at the calculated h as follows:

    The given equation is: y = - x^2 + 12x - 4

    Compute the result at x=h=6 to get k as follows:

    k = y = - (6) ^2 + 12 (6) - 4 = 32

    Therefore, based on the above calculations, the vertex form would be:

    y = a (x-h) ^2 + k

    y = - (x-6) ^2 + 32
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