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19 September, 22:04

Start off by building a basic coaster! Build a polynomial that: has an - intercept at x = 500. rises to a maximum, falls as it crosses the x-axis, and then rises into x = 1000. y = ax (x - ) (x - 1000)

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  1. 20 September, 01:44
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    Answer: the missing factor is (x - 500) and the whole function is:

    y = a x (x - 500) (x - 1000)

    Explanation:

    The question, if complete, is to find the missing factor.

    There are 4 factors: a, x, (x - ?), and x - 1000

    - a is a constant, which may take any value, unitl more information is given.

    - x factor means that there is an x-intercept at x = 0

    - x - 1000 factor means that there is an x - intercept at x = 100.

    - The condition of an x-intercept at x = 500 means that x - 500 is a factor.

    So, the factor missing is x - 500.

    And you can write y as:

    y = ax (x - 500) (x - 1000).

    See, that for x = 500 that becomes y = a (00) (500 - 500) (500 - 1000).

    ⇒ y = a500 (0) (-500) = 0, which is what x-intercept means.
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