Question

Help Please!!!
Using those points as zeros, construct the polynomial function, f(x), that will be the path of your rollercoaster. Show all of your work.

Answer 1

Welcome to Oakville Lake Amusement Park!
As one of the new rollercoaster engineers, you have been tasked with developing a rollercoaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the rollercoaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground. There must be three distinct points where the rollercoaster crosses the x–axis. Precise measurements and attention to detail are very important.

First, here is the existing map of current structures. It is important that the rollercoaster does not go through the foundation of any of these structures. Pick three points on the x–axis that the rollercoaster will dive underground or resurface. (Points that have a building on them are off-limits.)
1. The rollercoaster will run from right to left, so work in that order when selecting points.
• 1st point:___-8___
• 2nd point:___-2___
• 3rd point:___6___

This is the first bit

Answer 2

Is there a diagram for the question ?

Answer 3

yeah can you see it now?

Answer 4

(-8,-2,6) are your answers ??

Answer 5

those are the points I chose to cross the x axis

Answer 6

"...The rollercoaster will run from right to left..."
Also choose only one point between two buildings.

Answer 7

so my points would be 6,-2,-8?

Answer 8

Your order ^^ is correct, but I think the question asks for only one point between two buildings.

As there can be multiple answers; I am working with a general example.
Let the points be a, b, c

Then the polynomial function will be f(x) = k(x-a)(x-b)(x-c)

Answer 9

so for question two i can put f(x)= k(x-6)(x-(-2))(x-(-8)) ?

Answer 10

Q3 - You can do by yourself (IDK what theorems you have learnt)
Q4 - y intercept = f(0)
Q5 - Find the h(x) = 0 and g(x)=0 (See if they intersect x-axis at points having buildings)

PS: As for the selection of points; I am not really sure what does this means >> "...For one of the more thrilling sections, the rollercoaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground...."

Answer 11

@e.mccormick
Can you help here ??

Answer 12

for the fourth question, do I solve for x? if so, what do i do with the k?

Answer 13

@whpalmer4 could you help me out here?

Answer 14

@Compassionate
See the attached doc.
How can we choose the three points of intersection?
Do we also need to account for the height of the buildings? (for finding k)

Answer 15

really any help on this is appreciated. It doesn't even have to be a full answer i just need to understands some things.