Multiple Choice Question (MCQ)

The parabola with the equation y=4x-\dfrac{1}{2}x^2 has how many points with (x,y) coordinates that are both positive integers?

  1. ×

    3

  2. ×

    4

  3. ×

    7

  4. ×

    8

  5. ×

    Infinitely many

Collected in the board: Coordinate geometry

Steven Zheng posted 2 months ago


Answer

  1. If y>0, 4x-\dfrac{1}{2}x^2>0

    x(8-x)>0

    x(x-8)<0


    \therefore 0 < x<8

    \because y = 4x-\dfrac{1}{2}x^2


    In order for y to be integers, x must be even numbers.

    So x could be 2, 4, 6


    A is the choice.

Steven Zheng posted 2 months ago

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