Please help as soon as possible! THIS IS 45 POINTS
For the answer I find most helpful and easy to understand, I will mark Brainliest.
Ima try this one more time


Roller Coaster Crew

Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.

Part A

The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.

1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.

2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)

3. Create a graph of the polynomial function you selected from Question 2.


Part B

The second part of the new coaster is a parabola.

4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.

5. Create a graph of the polynomial function you created in Question 4.


Part C

6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.

Answer:

See Explanation

Step-by-step explanation:

Part A

Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.

Yes, they both can be correct. Ray is correct because you can have 4 intercepts. Only 3 can be zeros and 1 can be the Y-Intercept.

Part A - 2

Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.

The zeros of function g(x)= x^3-x^2-4x+4 is -2,2, and 1. The other key features of polynomial functions include end behavior, Y- intercept and the axis of symmetry, and the vertex.

Provide a sketch of g(x), Label or identify the key features on the graph.

Part b

pART B

Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.

The direction of the parabola would be both sides going up because they are the leading coefficient and the degree is both even and positive numbers. The zeros are 1.5 and -2. The Y-intercept is 6

The axis of symmetry is -1.75 and the vertex is 1.75 and 12.37

X= B/2A

X=7/2(2)

X= 1.75

2x^2+7X+6

2(1.75)^2+7(1.75)+6

2(-3.06)-12.25+6

-6.12-12.25+6

=12.37

The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.

Create a graph of the polynomial function you created in Question 4.

TOPIC 3

part c

Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.

Ray and Kelsey's new amazing roller-coaster!

Part d

*Reporter: So I hear you guys have this amazing roller-coaster that will be ready soon? Tell us all about it.

*Kelsey: Yes, We are so excited! We really took our time to make sure we build the best roller coaster ever and to see that Ray made sure everything is ready it's so wonderful and I know everyone will love it.

*Ray: Yea Kelsey is right we certainly took our time with it, It's gonna be the most epic ride yet! so everyone tell your friends!

*Reporter: Well we all can't wait to see it and take a ride!

Hope You Helped It :)

Consider f(x) = 3x. Describe how the graph of each function compares to f.

A construction company is building the house show below. They need to use a scale of 1 in: 8f. They measured the drawing to find that that the height of the building is 2.5 in. Explain to the construction workers how they would use this information for calculate the height of the final building.

I need help asap and no links please

Maggie cut out 4 right triangles of equal size from construction paper. Each right triangle has a base of 6 inches and a height of 8 inches. What is the total area, in square inches, of all the triangles combined?

HELP PLS

G.O and his neighbors clear a rectangle area 8 1/2 feet by 6 1/4 feet to plant shrubs. Now they have to decide how many shrubs to plant and how much water to use on the shrubs. shrub planting instructions: each shrub needs an area of about 2 square feet. each shrub will need about 1.25 liters of water a week. how many shubs should G.O plant? how much water will the shrubs need?

An 18-inch mushroom pizza sells for $18 at a pizza store. At a corner store, the same 18-inch mushroom pizza sells for $15. For the same mushroom pizza, the cost at the pizza store is about how many times as great as the cost at the corner store?

A. 1.8
B. 1.6
C. 1.2
D. 0.9

Need Help!
The 12 students in the Environmental Club represent 10% of the students in the seventh grade. How many students are in the seventh grade?

wuts 6 times 3 (no links)

What is the area of the ice skating rink

The answer choices are 32, 12, 18, 24 please help i cant fail this test

Which function has a range of f(x) ≤ 3/4?
A. f(x) = 3/4 x + 5
B. f(x) = -x^2 + 3/4
C. f(x) = x^2 - 3/4
D. f(x) = 3/4 - 5x

Identify the percent of change as an increase or decrease. Then find the percent of change. Round to the nearest tenth of a percent, if necessary.

72 people to 36 people

I have really bad allergies and I can’t focus, I’m extremely flustered. Can you please help?

The table shows the number of wins of each school baseball team over the last six years. Find the mean absolute deviation for each set of data. Round to the nearest hundredth if necessary. Then write a few sentences comparing their variation. Number of wins per season, Bears:7, 10, 13, 12, 9 Saints:12, 15, 10, 14, 13

Help splspsplspsw sjsplspsls

If the angle of R and the angle of S are vertical angles and the measure of Angle R = 39 degrees, what is the measure of angle S

Help ASAP i need the answer to this question plsss NO LINKS AND NO DOING IT JUST FOR THE POINTS Will give brainliest and just because i say don't do it just for the points doesn't mean i don't want you to do it i'm just saying that because i don't want random answers i want the right answers with work shown I need the whole page plsss its due today

On a recent math test a teacher asked for the measure of

Please help :( I need this today.

The x-intercept is the point on the x-axis where the line crosses it. The y-coordinate of the line's x-intercept is always zero. The x-coordinate of the x-intercept is the number where it crosses the x-axis. A line with an x-intercept of (5,0) crosses the x-axis at the number 5. A line with an x-intercept of (-5,0) crosses the x-axis at -5. Which of these coordinates could be a line’s x-intercept?

update for the second one

At 78°F, a certain insect chirps at a rate of 106 times per minute, and at 81°F, they chirp 112 times per minute. Write an equation in slope-intercept form that represents the situation.

The common hamster has 20 chromosomes. How many different types of hamster offsprings could form

i only need help on number 8 please

I need help plz
I will give you 50 points if it is right

The dad has a son and a daughter. The daughter is 19 years younger than the son. The son is 13 years younger than the dad (Don't ask, just keep reading.) The daughter is 21 years old now. How old is the dad?
Dad - 13 years older than son
Son - 19 years older than daughter
Daughter - 21 years old

im horrible at math

A parallelogram always has four congruent sides.
Group of answer choices

True

False

Flag question: Question 2
Question 21 pts
A rhombus is a parallelogram.
Group of answer choices

True

False

Flag question: Question 3
Question 31 pts
A rectangle is a square.
Group of answer choices

True

False

Flag question: Question 4
Question 41 pts
A rhombus is a quadrilateral.
Group of answer choices

True

False

Flag question: Question 5
Question 51 pts
A rectangle is a parallelogram.
Group of answer choices

True

False

Flag question: Question 6
Question 61 pts
The diagonals of this quadrilateral are congruent. (Select all that apply.)
Group of answer choices

rhombus

square

trapezoid

rectangle

parallelogram

Flag question: Question 7
Question 71 pts
This quadrilateral is a special type of rectangle and rhombus. (Select all that apply.)
Group of answer choices

parallelogram

rectangle

square

rhombus

trapezoid

Flag question: Question 8
Question 81 pts
All four angles of this quadrilateral are right angles. (Select all that apply.)
Group of answer choices

rhombus

rectangle

parallelogram

square

trapezoid

Flag question: Question 9
Question 91 pts
All four sides of this quadrilateral are congruent. (Select all that apply.)
Group of answer choices

rectangle

rhombus

trapezoid

square

parallelogram

Flag question: Question 10
Question 101 pts
This quadrilateral may have zero or two right angles. (Select all that apply.)
Group of answer choices

rectangle

parallelogram

rhombus

trapezoid

square

Justus owes $500 to his uncle for money he borrowed to go on vacation, $1,500 on his car, and $674 on his credit card. How much are his total liabilities?

(This is for my College Career Readiness class so im not sure which subject it falls under)

HEEELLLPPPP PLLLZZZ TT^TT

A salesman pays $20 for shirts and then sells them for $25. By what percent did he increase the price
compared to the original price?

Can someone explain why i got this answer wrong and how to get the answer!
And please someone help me

helpppppppp plzz :))))))