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Math Help - Calculate the area of a part of a function

  1. #1
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    Calculate the area of a part of a function

    Hi!
    I have this task:
    y=x^2-12x+36.36
    Find all squares that has 2 points on this function and 2 points on the x axis.

    I thought this task with using simply y=x^2
    To find at which point there is a square I thought a simple equation: 2x=y ; 2x=x^2
    2x because the distance is the same on both sides.

    Equation gave me result 0 and 2.

    x^2-12x+36.36=2x didn't give me the right result.
    Any other ideas?
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  2. #2
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    In order that the four points form a rectangle, they must be symmmetric about the vertex. Your method worked for y= x^2 has vertex (0, 0).

    Complete the square in y=x^2-12x+36.36 to determine the vertex, (x_0, y_0). You want to find "h" so that the distance from x_0- h to x_0+ h, 2h, is the same as the height y= (x_0+ h)^2-12(x_0+ h)+36.36
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  3. #3
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    y=x^2-12x+36.36
    x0=-b/2a = 12/2=6

    2h = (6+h)^2 - 12(6+h) + 36.36
    Microsoft Math says that h = 1.8 and 0.2

    So the area will be (2h)^2
    Thanks!
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