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Graphing Quadratic Relations Algebraically
Graph the following quadratic relations algebraically by finding each of the key features listed.

x^2−5 x+4
1. y-intercept
2. Zeroes (x-intercepts)
3. Axis of Symmetry
4. Vertex
5. Maximum/Minimum value

x^2−5 x+6
1. y-intercept
2. Zeroes (x-intercepts)
3. Axis of Symmetry
4. Vertex
5. Maximum/Minimum value

x^2−x−6
1. y-intercept
2. Zeroes (x-intercepts)
3. Axis of Symmetry
4. Vertex
5. Maximum/Minimum value

x^2−10 x+25
1. y-intercept
2. Zeroes (x-intercepts)
3. Axis of Symmetry
4. Vertex
5. Maximum/Minimum value

Determine (fg)(x) if f(x) = 5 - 2x and g(x) = 3x + 1

Type the coefficients of your final solution in form

s=-1/2 gt²+v₀ t+s₀, where s is the height of the objected at time t seconds, g is 32 feet per second² and v₀ and s₀ are the initial velocity and initial height, respectively. Two friends are in competition. Each stands on the roof of the apartment building where each one lives. At the same time, each friend stands at the edge of the roof and throws up a basketball as hard as possible. Joan's apartment building is 120 feet high, and she trows the basketball at a speed of 24 feet per second. Joe's apartment building is 105 feet high, and he trows the basketball at a speed of 30 feet per second. a)write the function that describes the height of Joan's basketball, in terms of time measured in seconds. What kind of function is the height function? How do you know? b)Display the graph of the function you found from a) above.

Fit a Parabola: points (1,-10), (2,-30), (-2,2). a)Find the equation of the unique parabola that passes through the three points given. You must show all the algebra necessary to find the equation. b)Use substitutions to verify that each point satisfy the equation you found.

A uniform bar of weight 30 N and length 4m passes over a prop and is supported in a horizontal position by a force of 10 N acting vertically upwards at the other end. Find the distance of the prop from the center of the bars.

Has Globalization affected poverty in a positive or negative way?

For the given functions f and g, complete parts (a)-(h). For parts (a)-(d),also find the domain.

f(x)=4x+7/7x-4; g(x)=7x/7x-4

a)find (f+g)(x). Simplify, what is the domain f+g?

b)find (f-g)(x). Simplify, what is the domain f-g?

c) find (f.g)(x). Simplify, what is the domain of f.g?

d)find (f/g)(x). Simplify, what is the domain of f/g?

e) find (f+g)(3).

f) find (f-g)(4).

g)find (f.g)(1).

h)find (f/g)(2).

Check my answers if they are correct pls asap!

Find the force required to move a load of 30N up a rough inclined plane, applied parallel to the plane. The inclination of the plane is such that when the same body is kept on a perfectly smooth plane inclined at an angle, a force of 6N applied at an inclination of 30" to the plane keeps the same in equilibrium. Assume coefficient of friction between the rough plane and the load is equal to 0.3.

Suppose that f(x) =x^2-3x+2 and g(x)-x^2-4 a. Determine (f+g)(x) and simplify, and find its domain. b. Determine (f-g)(x) and simplify and find its domain. c. Determine (f/g)(x) and simplify, and find its domain.

Determine (fg) (x) if f(x)= 5 - 2x and g(x) = 3x + 1.

In the space provided, type the coefficients of your final solution in  form.

(fg)(x) = ____ + ____x + ____ 

Case study:

One of the new ventures that Health Buddy Shop is providing prepared food for people who are into keto diet. The management will have its operations meeting sometime next time and it needs to approve its operational expenses which will include the budget for eparing their meal according to the required calaries per person  to attain a particular weight.  Mr. Angelo  has been tasked to handle the operations including the logistics part  which includes  the supplies and raw materials.  Initially, Mr Angelo has come from similar restaurant where ordering on a monthly basis is effective for them in terms of meeting customer requiremnets and meeting the least cost. With this experience, Mr Angelo followed the  same practices from that previous experience and began ordering  food boxes, disposable spoon and fork and paper cups monthly  with a fixed  order quantity of 2,000 pcs per order. Annual demand for the food is also equated to the usage and demand for the said materials which is 24,000 pcs annually.  Food boxes costs  BD 0.150, spoon and fork is BD0.30 while paper cups cost BD 0.20 Maintaing such a volume of materials costs the company BD 5.00 while the cost of ordering from supplier is Bd 12. Mr Angelo wants to ensure that what he will present to the management is correct so he has asked his other friends to  check and validate which in return agreed with his strategy. At its operations meeting, Mr. Angelo intend to declare that the practice is going to save money for the company. However, just before the operations meeting, a trainee named Mr. Rey has come and has been instructed to assess the operations and propose possible improvements that will ensure product quality and at the same  time saving money . Mr . Rey, who is a graduating student of MS Manufacturing  Management saw that there is something wrong with the proposed strategy that Mr. Angelo will implement in terms of order quantity. He objects the practice that is being done when it comes to ordering the food boxes, spoon and for and paper cups.

Answer the following Questions.

1. What is the impact that Mr Angelo’s strategy on the total cost   
2. What is the impact of Rey’s  idea in terms of ordering  inventories. 
3. Having seen the results in Q1 and Q2, what can you conclude to be the best strategy that the company should use? Support your answer with  data 

Kyla is a 4 year old child who has been in your day care program for about 7 months. She has been a pleasure to have in your program as she has been well mannered and even tempered. She has bonded well with other children and plays appropriately with them. In the last three weeks you have noticed a change in her temperament. She has been crying frequently and for no apparent reason. She no longer wants to play or engage in any way with the other children and she is unable to rest during nap time. She often lashes out at the other children by hitting, pushing or biting them.

Describe possible causes for this change in behavior and outline a course of action you could follow to learn more and Kyla’s behavior and possible referrals.