Mathematics > QUESTIONS & ANSWERS > Advanced Single-Variable Quadratic Equations and Complex Numbers (All)

Advanced Single-Variable Quadratic Equations and Complex Numbers

Document Content and Description Below

Advanced Single-Variable Quadratic Equations and Complex Numbers This activity will help you meet these educational goals: Mathematical Practices— You will make sense of problems and solve them, ... reason abstractly and quantitatively, use mathematics to model real-world situations, attend to precision, look for and make use of structure, and express regularity in repeated reasoning. Introduction Most functions used to model real-world situations are either linear or quadratic in nature. Linear and quadratic equations are used in business, economics, science, and other fields. Factoring polynomials can help you find unknown quantities. In this activity, you will solve linear and quadratic functions to find unknown values. __________________________________________________________________________ Directions and Analysis Task 1: A Garden Shop Liam, a garden shop owner, sells a variety of plants. He needs to determine the price for chrysanthemums that will earn the maximum profit for his business. After doing some research on how mums are priced by competitors, he arrives at the function x f p p    ( ) 90 10 , which models the relationship between units of mum sold in a week (x) and the corresponding price (p). Using the function x = 90 – 10p, you can see that the number of units of mums sold (x) varies with the price (p). As the price increases, the number of units sold decreases, as shown in the table. The price cannot be negative, so there are only nonnegative values for p. Likewise, the number of units sold cannot be negative, so the table includes only values of p that give a nonnegative output for x. Price (p) in $ Units of Mums ( x p   90 10 ) 0 90 1 80 2 70 3 60 4 50 5 40 6 30 7 20 8 10 1 This study source was downloaded by 100000849847893 from CourseHero.com on 07-14-2022 16:01:16 GMT -05:00 https://www.coursehero.com/file/22916519/A5-Advanced-Single-Variable-Quadratic-Equations-and-Complex-Numbers-UA-2/9 0 a. Liam wants to know how the function x f p p    ( ) 90 10 would need to change to reflect the amount of money the business will take in. Use this function to model a function for gross sales. (Gross sales are the total amount of money the flowers sell for.) Type your response here: b. Liam knows that his cost (c) in terms of the units of mums sold (x) can be modeled by the function c x x ( ) 60 .   Replace the variable x in this function with the function that gives the number of units sold (x) in terms of price p. What does this turn the function c into? Type your response here: c. Liam wants to calculate the profit his shop would earn from the sale of mums. He knows that it can be done by deducting the costs from the money that the store makes selling mums. Now that he has the functions for the cost and gross sales, can he subtract the function for cost from the function representing the gross sales to arrive at a function for profit? Why? Type your response here: d. Find the store’s profit function for selling mums by subtracting the function for cost from the function for gross sales. Consider pr(p) as the profit function. [Show More]

Last updated: 2 years ago

Preview 1 out of 6 pages

Buy Now

Instant download

We Accept: