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Grade 12 Advanced Functions, University Preparation (MHF4U)
C. Polynomial and Rational Functions
43. 12AF.C3.7
43.1 Applications of polynomial functions
Applications of Polynomial Functions
Polynomials model real quantities like area, volume, and revenue -- with the same tools you already know.
What You'll Learn
Polynomials model real quantities: area, volume, revenue, and projectile height.
Worked example: folding a cut sheet into a box gives volume V(x)=x(20-2x)(12-2x).
The box volume is a cubic polynomial in the cut length x.
Revenue (price times quantity) and projectile height are common polynomial models too.
Once a scenario is a polynomial, the usual factoring and graphing tools apply directly.
What You'll Practice
1
Creating volume formulas from geometric constraints with cut-out dimensions
2
Graphing polynomial functions and identifying realistic domain restrictions
3
Finding maximum values and corresponding x-values using calculator tools
4
Solving age-based word problems by assigning variables and setting up equations
Why This Matters
Polynomial functions model countless real-world situations, from engineering design and manufacturing to financial planning and population growth. Mastering these applications develops your problem-solving skills and prepares you for advanced math, science, and business courses where optimization and modeling are essential.
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Polynomial Functions
Word Problems
Volume Calculations
Domain and Range
Optimization
Graphing
Variable Assignment
Real-World Modeling
ON Curriculum Aligned