algebra

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determine the given quadratic function has a minimum valueor maximum vale. Then find the coordinates of the minimum or maximum point.
f(x)=x^2=2x-9

  • algebra -

    Your parabola opens up because of +x^2, so it has a minimum

    to find min, 3 methods:

    1. by Calculus,
    f ' (x) = 2x + 2
    = 0 for a min of f(x)
    2x = -2
    x=-1
    f(-1) = 1 - 2 - 9 = -10

    2. complete the square to find the vertex:
    f(x) = x^2 + 2x + 1 -1 -9
    =(X+1)^2 - 10
    the vertex is (-1,-10)
    so there is a min of -10 when x = -1

    3. by formula
    if f(x)= ax^2 + bx + c, the x of the vertex is -b/2a
    x of vertex = -2/(2(1)) = -1
    f(-1) = -10 , as above

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