College Algebra: Polynomials and Functions – Syllabus and Study Guide (MAT 112A)

Course Overview

Course Description

This course, Algebra: Polynomials (MAT 112A), focuses on solving application problems involving linear, quadratic, and power equations, and analyzing graphs of linear, quadratic, and power functions. The course is designed to develop students' algebraic skills and quantitative reasoning, preparing them for further studies in mathematics and related fields.

• Credit Hours: 1.5

• Prerequisites: Completion of MAT 098 or 110 with a grade of “C” or better, or appropriate placement scores.

• Co-requisite: MAT 111A for students not meeting the mathematics readiness indicator.

Student Learning Outcomes (SLOs)

• Solve applied problems modeled with linear and quadratic equations and inequalities.

• Analyze real-life problems using mathematical modeling.

• Graph and interpret data represented by linear, quadratic, and power functions.

• Use numerical and graphical data to make reasonable and valid conclusions.

• Solve applied problems involving equations and inequalities with absolute value.

Essential Skills Developed

• Quantitative Reasoning: Use data to analyze and solve numerical problems.

• Information for Decision Making: Identify, evaluate, and responsibly use information to make decisions.

Course Topics and Schedule

The following topics are covered, aligning with standard College Algebra curriculum:

• Ch. 1 – Functions, Graphs, and Models; Linear Functions

  • 1-1 Functions and Models

  • 1-2 Graphs of Functions

  • 1-3 Linear Functions

  • 1-4 Equations of Lines

• Ch. 2 – Linear Models, Equations, and Inequalities

  • 2-1 Algebraic and Graphical Solution of Linear Equations

  • 2-2 Fitting Lines to Data Points: Modeling Linear Functions

  • 2-3 Systems of Linear Equations in Two Variables

  • 2-4 Solutions of Linear Inequalities

• Ch. 3 – Quadratic, Piecewise-Defined, and Power Functions

  • 3-1 Quadratic Functions; Parabolas

  • 3-2 Solving Quadratic Equations

  • 3-3 Power and Root Functions

  • 3-4 Piecewise-Defined Functions and Power Functions

  • 3-5 Quadratic and Power Models

• Ch. 4 – Additional Topics with Functions

  • 4-4 Additional Equations and Inequalities

• Ch. 6 – Higher-Degree Polynomial and Rational Functions

  • 6-1 Higher-Degree Polynomial Functions

  • 6-2 Modeling with Cubic and Quartic Functions

  • 6-3 Solution of Polynomial Equations

Key Concepts and Definitions

Functions and Models

• Function: A relation in which each input (independent variable) has exactly one output (dependent variable).

• Mathematical Model: An equation or function that represents a real-world situation.

• Example: The height of a ball thrown upward as a function of time can be modeled by a quadratic function.

Graphs of Functions

• Graph: A visual representation of the set of all ordered pairs (x, f(x)).

• Key Features: Intercepts, slope, vertex (for quadratics), domain, and range.

• Example: The graph of $y = 2x + 3$ is a straight line with slope 2 and y-intercept 3.

Linear Functions and Equations of Lines

• Linear Function: A function of the form $f(x) = mx + b$.

• Slope (m): The rate of change; $m = \frac{y_2 - y_1}{x_2 - x_1}$.

• Equation of a Line: $y = mx + b$ or $Ax + By = C$.

• Example: Find the equation of a line passing through (1,2) with slope 4: $y - 2 = 4(x - 1)$.

Solving Linear Equations and Inequalities

• Linear Equation: An equation of the first degree (e.g., $2x + 5 = 11$).

• Solution: Isolate the variable: $2x + 5 = 11 \implies 2x = 6 \implies x = 3$.

• Linear Inequality: An inequality involving a linear expression (e.g., $3x - 7 < 2$).

• Example: $3x - 7 < 2 \implies 3x < 9 \implies x < 3$.

Systems of Linear Equations

• System of Equations: Two or more equations with the same variables.

• Solution Methods: Substitution, elimination, or graphical methods.

• Example: Solve $\begin{cases} x + y = 5 \\ x - y = 1 \end{cases}$

  • Add equations: $2x = 6 \implies x = 3$

  • Substitute: $3 + y = 5 \implies y = 2$

Quadratic Functions and Equations

• Quadratic Function: $f(x) = ax^2 + bx + c$

• Vertex: The point $(h, k)$ where $h = -\frac{b}{2a}$ and $k = f(h)$.

• Solving Quadratic Equations: Factoring, completing the square, or quadratic formula:

  • $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Example: Solve $x^2 - 5x + 6 = 0$ by factoring: $(x-2)(x-3) = 0 \implies x = 2, 3$.

Power and Root Functions

• Power Function: $f(x) = ax^n$ where $n$ is a real number.

• Root Function: $f(x) = \sqrt[n]{x}$

• Example: $f(x) = x^{1/2} = \sqrt{x}$

Piecewise-Defined Functions

• Piecewise Function: A function defined by different expressions for different intervals of the domain.

• Example: $f(x) = \begin{cases} x^2, & x < 0 \\ x, & x \geq 0 \end{cases}$

Higher-Degree Polynomial Functions

• Polynomial Function: $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$

• Degree: The highest power of $x$ with a nonzero coefficient.

• Example: $f(x) = x^3 - 2x^2 + x - 5$ is a cubic (degree 3) polynomial.

Modeling with Functions

• Fitting Lines to Data: Using regression or other methods to find the best-fit line for a set of data points.

• Application: Predicting trends, making forecasts, or interpreting scientific data.

Assessment and Grading

Component	Weight
Midterm Exam	25%
Final Exam	35%
Quizzes/Instructor Grades	20%
Homework	20%

Grading Scale:

Grade	Percentage Range
A	≥ 90.00
B	80.00 ≤ B < 90.00
C	70.00 ≤ C < 80.00
D	60.00 ≤ D < 70.00
F, FN	< 60.00

Course Materials

• MyLab Math Access: Online homework and e-textbook platform.

• Calculator: Non-CAS graphing calculator (TI-84 recommended).

• Textbook (optional): College Algebra in Context by Harshbarger and Yocco, 6th edition.

Academic Integrity and Policies

• AI Use: Not permitted for any assignments or activities.

• Collaboration: All work must be your own unless otherwise specified.

• Calculator Policy: Only approved calculators allowed during exams; no uploading or saving course content to calculators.

• Attendance: Regular attendance and participation are expected for success.

Support Resources

• Mathematics and Statistics Tutoring Center (Wallace 342): Walk-in and online tutoring available.

• Student Success Center: Free tutoring, mentoring, and workshops.

• Center for STEM Excellence: Academic support, calculator loans, and study materials.

• EKU Libraries: Study spaces and research support.

Course Calendar (Tentative)

Week	Topics
Aug 24 - 30	Syllabus, 1.1, 1.2, 1.3
Aug 31 – Sep 6	1.4, 2.1, 2.2
Sep 7 – 13	2.3, 2.4
Sep 14 - 20	3.1, Review, Midterm Exam
Sep 21 - 27	3.2, 3.3, 3.4, 3.5
Sep 28 – Oct 4	4.4, 6.1, 6.2
Oct 5 - 9	6.3, Review, Comprehensive Final Exam

Exam Format

• Open-ended questions: Show all work for full credit.

• Multiple-choice questions: No work required to be shown.

• Permitted materials: Writing utensils and calculator only.

Additional Info

• This syllabus provides a comprehensive overview of the course structure, expectations, and resources for success in College Algebra (MAT 112A).

• For detailed explanations and examples of each topic, refer to the course textbook or MyLab Math resources.