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If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking

If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 21E
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#6- If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking(in image)

service, they estimate how much of that product or When a company offers a new product service people will want at different prices. This is referred to as the product or service demand. As the price of a product or service increases, the demand usually decreases, and this drives the price down. Companies use the estimated demand to determine how much of a product or service they are willing to supply at different prices. As the price of a product or service increases, companies are willing to supply more of it because they will earn more money. If you graph the demand and the supply curves on the same xy-plane, they will sometimes intersect at the point where the price and the supply are in equilibrium. Consider the scenario below. Yaseen is a local artist who wants to increase the amount of money she earns every month by selling at-home painting kits. These kits will include a photograph of the finished painting, a link and password to Yaseen's YouTube channel where she will provide detailed instructions and a step-by-step demonstration of how to create the painting. The kit also contains the canvas, and all the paints the buyer will need. Yaseen will create a new kit for sale each month. Yaseen estimates that the monthly demand for her painting kits can be modeled by the function f(x) = 0.02(x - 100)?, where 0 <x< 85. The number of kits that Yaseen can supply each month is modeled by the function g(x) = 0.01x² + 0.5x, where 0<x< 100. The value of x represents the quantity of kits and the output of each function is the price. Use this information and what you know about quadratic functions and systems of non-linear equations to explore the questions below. 1. Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario? demand function of price decrease from 200 to 4.5 demand 0 to 85 Supply function g(100)=0.01x100^2=150 supply price increases as x quantity (paint increases) 2. Suppose that in her first month Yaseen is able to create 15 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work. f(x)=0.02 (x-100)^2 , where 0 is less then or equal to x which is less than equal to 85 g(x)=0.01 (x)^2+0.05x where 0 is less than or equal to x which is less then or equal to 100 , will be selling product at g(15)=0.01 (15)^2+0.05 x15 f(15) = 0.02(15 – 100)^2 = $ 144.5 (per unit of drawing kit). charge per unit ss funvtion=$9.75. dd= 144.5 3. In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of business, she decides to supply 60 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work. g(x) = 0.01x^2+0.05x x =quantity sold by Yasin in second month x=60 units g(60) = 0.01(60^2)+0.05(60) = 0.01(3600)+0.05(60) = 36+3 = $39 per kit when x=60 4. If Yaseen creates 60 kits in her second month of business and offers them for sale at $66 each, do you think she will sell all of them? Why or why not? No she will not sell all of them because 66=0.02 (x-100)^2 x= +- sqaureroot 66/0.02 + 100 x=42.55 she can sell 43 kits. 5. What family of functions do f(x) and g(x) belong to? How do you know? Both the functions f(x) and g(x) are part of the quadriatic family as they both have a degree of 2. 6. If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking.
Transcribed Image Text:service, they estimate how much of that product or When a company offers a new product service people will want at different prices. This is referred to as the product or service demand. As the price of a product or service increases, the demand usually decreases, and this drives the price down. Companies use the estimated demand to determine how much of a product or service they are willing to supply at different prices. As the price of a product or service increases, companies are willing to supply more of it because they will earn more money. If you graph the demand and the supply curves on the same xy-plane, they will sometimes intersect at the point where the price and the supply are in equilibrium. Consider the scenario below. Yaseen is a local artist who wants to increase the amount of money she earns every month by selling at-home painting kits. These kits will include a photograph of the finished painting, a link and password to Yaseen's YouTube channel where she will provide detailed instructions and a step-by-step demonstration of how to create the painting. The kit also contains the canvas, and all the paints the buyer will need. Yaseen will create a new kit for sale each month. Yaseen estimates that the monthly demand for her painting kits can be modeled by the function f(x) = 0.02(x - 100)?, where 0 <x< 85. The number of kits that Yaseen can supply each month is modeled by the function g(x) = 0.01x² + 0.5x, where 0<x< 100. The value of x represents the quantity of kits and the output of each function is the price. Use this information and what you know about quadratic functions and systems of non-linear equations to explore the questions below. 1. Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario? demand function of price decrease from 200 to 4.5 demand 0 to 85 Supply function g(100)=0.01x100^2=150 supply price increases as x quantity (paint increases) 2. Suppose that in her first month Yaseen is able to create 15 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work. f(x)=0.02 (x-100)^2 , where 0 is less then or equal to x which is less than equal to 85 g(x)=0.01 (x)^2+0.05x where 0 is less than or equal to x which is less then or equal to 100 , will be selling product at g(15)=0.01 (15)^2+0.05 x15 f(15) = 0.02(15 – 100)^2 = $ 144.5 (per unit of drawing kit). charge per unit ss funvtion=$9.75. dd= 144.5 3. In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of business, she decides to supply 60 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work. g(x) = 0.01x^2+0.05x x =quantity sold by Yasin in second month x=60 units g(60) = 0.01(60^2)+0.05(60) = 0.01(3600)+0.05(60) = 36+3 = $39 per kit when x=60 4. If Yaseen creates 60 kits in her second month of business and offers them for sale at $66 each, do you think she will sell all of them? Why or why not? No she will not sell all of them because 66=0.02 (x-100)^2 x= +- sqaureroot 66/0.02 + 100 x=42.55 she can sell 43 kits. 5. What family of functions do f(x) and g(x) belong to? How do you know? Both the functions f(x) and g(x) are part of the quadriatic family as they both have a degree of 2. 6. If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking.
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