Math

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The following three points are produced by some quadratic function of the form :
f(x) = Ax^2 + Bx + C
where A; B and C are real numbers and A = 0; they are (1/2,0);(0,10); and (4,0). Find a quadratic
function that satisfy es these three points.

  • Math -

    Form the igven points, you see that at x = 1/2 and at x = 4 the function is zero. This means that the function is proportional to:

    (x - 1/2) (x - 4)

    So, we can put:

    f(x) = D (x - 1/2) (x - 4)

    To find D, you use that at f(0) = 10:

    f(0) = 2 D = 10 ----->

    D = 5

    Therefore:

    f(x) = 5 (x - 1/2) (x - 4) =

    5 x^2 - 45/2 x + 10

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