Graph of Cubic Function NOTE: Figure not drawn to scale. In the figure above, ABCD is a rectangle. Points A and C lie on the graph of y = px3, where p is a constant. If the area of ABCD is 4, what is the value of p ?

Show/Hide Answer

Answer:

p = 16 Level of Difficulty E M H There are several things to make note of before beginning work on this problem: ABCD is a rectangle whose sides are parallel to the x and y axes; the cubic graph goes through opposite corners of the rectangle; the given cubic polynomial is symmetric about the origin (it is an odd function). Given the observations above, we can conclude that the rectangle is centered about the origin and that the magnitude of a, b, c, and d are all the same. One way to express the height of the rectangle, therefore, is 2a. Notice the base of the rectangle has length = 1. Area = base x height; 4 = (1)(2a); a = 2. Therefore, 2 is the distance of the rectangle above and below the x axis. Let's label point A with its coordinates: (-1/2, -2). This point must satisfy the cubic equation because it lies on the graph of that function. After plugging in: -2 = p(-1/2)3 Solving for p, you should get p = 16.

For more information on cubic equations, see the article All Cubic Polynomials are Point Symmetric. Our SAT tutors can help you become very proficient with all types of math SAT questions.

Earn 5% cash for every purchase you refer.

Latest News

Read All News
April 20, 2021

New subject available! Quantitative Methods

Hey students!  24HourAnswers.com is proud to annouce that we've added another topic to our Business subject area. You can now receive online tutoring for Quantitative Methods. You can learn more about Quantitative Methods at https://www.24houranswers.com/subjects/Business/Quantitative-Methods.   -24HourAnswers team
READ MORE
April 12, 2021

$500 College Scholarship Deadline

Just a reminder to our students and website visitors that the deadline for the Spring semester scholarship is May 1st. To learn more about applying, please visit our blog.  https://www.24houranswers.com/blog/75/24HourAnswers-500-Scholarship  
READ MORE
Live Chats