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? asked in Science & MathematicsMathematics · 9 years ago

ind the exact coordinates of the centroid for the region bounded by the curves y=4−x^2 and y=0 to balance?

Hi. I know that the x cordinate will be at the middle cause the shape is symmetrical, in this case x=0, but how do i solve where the point should be in the y axis? THanks a lot in advance for the help!

Update:

At the person below me, the question is not trying to solve for the y interception, but where should y be in between 0 and 4 in order to balance the parabola, if it were real and you had to use a finger to do it?

1 Answer

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  • Yoda
    Lv 5
    9 years ago
    Favorite Answer

    y = 4 - x^2 shows where the vertex for x is. When you have y = a - (x - b)^2, the x-coordinate of the vertex is b, and the y-coordinate is clearly at a. Here, there is no b, so it's 0.

    The y-coordinate is actually easy, all you have to do is solve for y. y = 4 - 0^2 = 4

    You really need to start using terms so I understand what you're saying. I think you're asking for the focus point.

    For y = ax^2 + bx + c, the focus point is at (-b/2a, c - (b^2 - 1)/4a)

    So for y = 4 - x^2, a = -1, c = 4

    So the focus point is at (0, 15/4)

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