Question

Can someone help me with one of my math problems ?

Answer 1

Post the question and someone will be happy to help. :)

Answer 2

Welcome to Oakville Lake Amusement Park!
As one of the new roller coaster engineers, you have been tasked with developing a roller coaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the roller coaster 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 roller coaster crosses the x–axis. Precise measurements and attention to detail are very important.

Answer 3

First, here is the existing map of current structures. It is important that the roller coaster does not go through the foundation of any of these structures.

1st point: ___6___
2nd point:___-2___
3rd point: ___-7___

Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your roller coaster. Show all of your work.

Answer 4

i don want just the answer i want someone to walk me thrugh this

Answer 5

Well, this one's a bit of a challenge, but I'm sure we'll get it. Give me a second. :)

Answer 6

Okaii ! I will appreciate !

Answer 7

Alright, see diagram attached. We know that the path goes through these points as given.

Answer 8

Make sense so far?

Answer 9

Yes

Answer 10

OK, then, this is probably what we want our path to end up looking like...

Answer 11

Now, let's look at the points that the polynomial goes through (-7,0), (-2,0), and (6,0). agree so far?

Answer 12

Im sorry !

Answer 13

okaii ! Yes i read ! it

Answer 14

No worries. :)

Answer 15

Now, we need to convert these points into "roots". What is mean is
(-7,0) -> (x + 7)
(-2,0) -> (x + 2)
(6,0) -> (x - 6)

Does that make sense? Those steps always used to confuse me when I was learning this. :)

Answer 16

So, f(x) = (x + 7)(x + 2)(x - 6)

Answer 17

dont i have to make it equal zero ?

Answer 18

Maybe, it depends on what you mean, how would you write it?

Answer 19

like x-6=0

Answer 20

right ?

Answer 21

Yes, that is how I went from (6, 0) to (x - 6). Because x = 6 means x - 6 = 0.

Answer 22

Ohh ! Okaii !

Answer 23

So, the formula will be each of those, giving us f(x) = (x + 7)(x + 2)(x - 6). (Not equal to 0 in the final formula since the rollercoaster is not always 0).

Answer 24

okaii

Answer 25

Now, are we done? Not quite. We found a f(x) like the question wanted, but we need to make sure that it actually works. :)

Answer 26

how ?

Answer 27

Well, let's test to make sure that at x = 10 for example, the roller coaster height is actually negative (underground).

Answer 28

we substitute 10 right ?

Answer 29

Yep. Let's see what we get.

Answer 30

f(10) = (10 + 7)(10 + 2)(10 - 6) = (17)(12)(4) = something not negative... uh oh... :)

Answer 31

How, do we fix this? Well, we can change our formula to f(x) = -(x + 7)(x + 2)(x - 6) by sticking a negative on the front, and this will fix our negative problem.

Answer 32

Notice, we keep all the "roots" the same, the negative just changes the height.

Answer 33

Does that make sense? It's a little tricky. :)

Answer 34

Im keeping up ! Buddy !

Answer 35

Excellent! :)

Answer 36

Alright, so the negative will make x = 10 work. Let's check x = 2 to see if that is positive (it should be).

Answer 37

f(2) = -(2 + 7)(2 + 2)(2 - 6) = -(9)(4)(-4) = positive. Yay!

Answer 38

Yaayy !!

Answer 39

I think you get the point, I'll let you check the two other crucial areas later, between -7 and -2 should be negative, to the left of -7 should be positive.

Answer 40

Well, Thank you ! You just helped me get started on my asigment !

Answer 41

You are welcome... one last thing I just thought of.

Answer 42

We don't want to crash into the castle at (-1, 2) about.

Answer 43

Yes !

Answer 44

Make sure that f(-1) is bigger than 2. :)

Answer 45

oh Okaii ! I Will ! Thank You !!

Answer 46

Good luck, if it isn't multiple the front by some number to "stretch" the graph. I think it should work though (that would be a really mean assignment). :)