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 )
Accepted Solution
A:
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.