Respuesta :
A multiplicity of a zero determines the behavior of a graph's x-intercept.
The coaster's needed polynomial is y = -ax(x - 500)(x - 1000)².
What is polynomial function?
The polynomial function is one that involves solely non-negative number powers of x, such as a quadratic, cubic, or quartic function. We can define a polynomial and give it a generic definition.
Now, according to the question;
The Parent function is given as; y = ax(x - 1000)
If (x - 500) is a factor of a polynomial, this polynomial crosses the x-axis, and we have;
y = ax(x - 500)(x - 1000)
Given that the graph would initially rise, its preceding coefficient is negative resulting in;
y = -ax(x - 500)(x - 1000)
To get the polynomial will come in smoothly and stop at y = 0, we need to introduce a bump here on x-axis with a factor for 1,000 at x = 1,000 of (x - 1,000)².
As a result, the needed polynomial is y = -a·x·(x - 500)·(x - 1000)².
A height of the preceding polynomial decreases as x approaches 1,000, because the factors (x - 500) and (x - 1,000) get smaller.
Therefore, a multiplicity of a zero determines how a graph's x-intercept behaves.
To know more about polynomial function, here
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The correct question is-
Here's another coaster that will help you think about the effect of a factor's exponent!
Once again, make the coaster cross at x = 500 after an initial rise and fall.
This time, make your track more realistic: make the coaster come in smoothly at x = 1000 instead
of just falling and suddenly stopping!
y = Flax(x – 1000)
