To state: A quadratic function to represent the area of all rectangles with a perimeter of 36 ft. Then graph the function and describe the rectangle that has the largest area.
The quadratic function that represents the area of all rectangles is
Given information:
The given perimeter of a rectangle is 36ft.
Explanation:
Let’s assume x as the length of the rectangle and y as the width of the rectangle.
Then the perimeter of the rectangle is:
Now the area of the rectangle is:
Now plot the function
This function will have value 0 at,
The resultant graph looks like a parabola and it has its maximum at
Then,
Now the maximum area will be:
Therefore, the maximum area is 81 square feet.
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)