here's another coaster that will 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)

The behavior of the x-intercept of a graph is given by the multiplicity of the zero

The required polynomial for the coaster is, y = -a·x·(x - 500)·(x - 1000)²

Reason:

The question relates to the introduction of characteristics to the graph of a polynomial through knowledge of the effect of parameters of a polynomial

Known parameter:

Parent function is, y = a·x·(x - 1000)

The polynomial crosses the x-axis when (x - 500) is a factor of the polynomial, therefore, we have;

y = a·x·(x - 500)·(x - 1000)

Given that the graph is to initially rise, the leading coefficient is negative, therefore, we have;

y = -a·x·(x - 500)·(x - 1000)

For the polynomial to come in smoothly to stop at y = 0, when x = 1,000 we have that a turning point of the polynomial will be located at x = 1,000, this is given by introduction of a bump on the x-axis at x = 1,000 with a factor of (x - 1,000)²

Therefore, the required polynomial is y = -a·x·(x - 500)·(x - 1000)²

The height of the above polynomial is progressively smaller as x tends towards 1,000, given that the factors, (x - 500), and (x - 1,000), becomes smaller.

Learn more about the graph of polynomial functions here:

link

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

22.83 repeating

step-by-step explanation:

137 ÷ 6 is 22.8333333 therefore we understand that 3 is repeating.

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