Math

find the vertex line of symmetry the minimum naximum value of the quadratic function and graph the function f(x)=-2x^2+2x+2.

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  1. A parabola has either a minimum or a maximum, but not both.

    The axis of symmetry, which contains the vertex, is the line

    x = -b/2a = -2/(-4) = 1/2

    You should now be able to get the max/min and thus the vertex

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  2. Express the function in canonical form by completing squares:
    if f(x)=a(x-h)²+k,
    then
    a>0 => the parabola is concave up, hence a minimum exists
    a<0 => concave down, hence a maximum.
    The location of maximum/minimum is given by the point (h,k).
    The line of symmetry is x=h.

    To proceed with completing the squares, extract and factor out the coefficient of x²:
    f(x)=-2(x²-x) + 2
    =-2[(x-1/2)²-(1/2)²]+2
    =-2[(x-1/2)²]+5/2
    So the curve is concave down, h=1/2, k=5/2 and (h,k)=(1/2,5/2) is a maximum.
    The line of symmetry is x=1/2.

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  3. How do I find the Y coordinate and the x coordinates

    is the vertix 1/2, 5/2?

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  4. By completing squares, we get the two parameters h and k which represent the x- and y-coordinates of the vertex.
    In this case, they are (1/2,5/2), as you can see from:
    f(x) = -2[(x-1/2)²]+5/2

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