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##### MATH 133 Unit 2 - Individual Project Assignment - Quadratic Equations

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Question;MATH 133 Unit 2 - IndividuRemember that the;standard form for the quadratic function equation isy=f(x);=ax2+bx+cand the;vertex form isy=f(x) =a(x?h)2+k;where (h,k) are the coordinates of the vertex of this;quadratic function?s graph.;You will use P(x);=?0.2x2+ bx? cwhere (?0.2x2+ bx);represents the business? variable profit and cis the;business?s fixed costs.;So, P(x);is the store?s total annual profit (in $1,000) based on the number of items;sold, x.;1.;Choose a value between;100 and 200 for b. That value does not have to be a whole number.;2. Think about and list what the fixed costs might;represent for your fictitious business (be creative). Start by choosing a fixed;cost, c, between $5,000 and $10,000, according to the first letter;of your last name from the values listed in the following chart;3.;Replace band cwith;your chosen values in Parts 1 and 2 in P(x) =?0.2x2+ bx? c.;This is your quadratic profit model function. State that quadratic profit model;functions equation.;4.;Next, choose 5 values;of x(number of items sold) between 500 and 1,000. Think about;the general characteristics of quadratic function graphs (parabolas) to help;you with choosing these 5 values of x.;5.;Plug these 5 values into;your model for P(x), and evaluate the annual business profit;given those sales volumes. (Be sure to show all of your work for these;calculations.);6.;Use the 5 ordered pairs;of numbers from 5 and 6 and Excel or another graphing utility to graph your;quadratic profit model, and insert the graph into your Word answer document.;The graph of the quadratic function is called a parabola.;7.;What is the vertex of;the quadratic function graph? (Show your work details, or explain how you found;the vertex.);8.;What is the equation of;the line of symmetry? Explain how you found this equation.;9.;Write the vertex form;for your quadratic profit function.;10.;Is there a maximum;profit for your business? If so, how many items must be sold to produce the;maximum profit, and what is that maximum profit? If your quadratic profit;function has a maximum, show your work or explain how the maximum profit figure;was obtained.;11.;How would knowing the;number of items sold that produces the maximum profit help you to run your;business more effectively.;12.;Analyze the results of;these profit calculations and give some specific examples of how these;calculations could influence your business decisions.;14. Which of the intellipathLearning;Nodes seemed to be most helpful in completing this assignment?;Suppose that you need to;fence a rectangular play area in your backyard for your child or pet. Further;suppose that you know the length must be 8 feet longer than the width. The back;of your house will serve as one side of the fenced area.;Note:The perimeter (distance around) of a general;rectangle is P= 2L+ 2W, and its area;is A= Lx W. In this;situation, P= L+ 2W.;1. Based on the first;letter of your last name, choose a value for your backyard area that must be;fenced from the range corresponding to the first letter of your last name;indicated in the following table.l Project Assignment - Quadratic Equations

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