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HOW DO I SOLVE QUADRATIC EQUATIONS WITH A TI-89?

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Course Content and Outcome Guide

DATE: April 17, 2003
COURSE NUMBER: MTH 95
COURSE TITLE: Intermediate Algebra
CREDIT HOURS: 4
LECTURE HOURS PER WEEK: 3
LECTURE/LAB HOURS PER WEEK:    2
LAB HOURS PER WEEK:           
NUMBER OF WEEKS: 10
SPECIAL FEE:                   

 

 PREPARED BY: Linda Bastian, Kandace Kling, Ilga Ross, Pauline Siekas, Janet Muzos, Mathew Funk, John Evans, Kanchan Mathur

COURSE DESCRIPTION FOR PUBLICATION:  
Functions are investigated graphically, numerically, symbolically and verbally in real world settings. Linear, quadratic and exponential functions are explored. Technology is integrated into all aspects of the course, as appropriate. Students communicate results in oral and written form. Graphing calculator required TI-89 recommended.
Prerequisite: Successful completion of MTH 65 and placement into WR 115.

INTENDED OUTCOMES FOR THE COURSE:

  • Creatively use mathematical and other problem solving strategies to formulate problems, to solve problems using multiple approaches, and to interpret results.
  • Make mathematical connections by recognizing and creating linear, quadratic, and exponential models of nontrivial real world situations.

  • Demonstrate mastery of linear and quadratic functions.

  • Meet the prerequisites for the study of college-level mathematics.

COURSE ACTIVITIES AND DESIGN:
All activities will follow the premise that formal definitions and procedures evolve from the investigation of practical problems. In-class time is primarily activity/discussion emphasizing problem solving techniques. Activities will include group work.

OUTCOME ASSESSMENT STRATEGIES:
 Assessment shall include:

  1. At least two proctored, closed book examinations.
  2. Assignments that offer an opportunity to express mathematical concepts in writing.
    Assessment should be made on the basis of using correct mathematical syntax, appropriate use of the English language, and explanation of the mathematical concept.
  3. At least two of the following additional measures:
a. Take-home examinations. 
b. Graded homework. 
c. Quizzes. 
d. Group projects. 
e. In-class activities. 
f. Attendance. 
g. Portfolios. 
h. Individual projects. 
i.  Individual student conference.

COURSE CONTENT (Themes, Concepts, Issues, Competencies, and Skills):

THEMES:

  • Linear, quadratic, and exponential functions
  • Graphing
  • Algebraic manipulation of rational and radical equations, including complex fractions
  • Technology
  • Problem solving
  • Critical thinking
  • Communication
  • Group work

  • Data analysis

SKILLS:

1.0 FUNCTIONS
The goal is to investigate functions represented graphically, symbolically, numerically and verbally in real world settings. Technology shall be integrated, as appropriate, in all aspects.       

1.1 Given a function represented graphically:
1.1.1 Identify and interpret the domain and range of the function.
         1.1.1a  Use interval notation to describe the domain and range of a function.

1.1.2 Identify and interpret the horizontal and vertical intercepts of a function.

1.1.3  Evaluate f(a), solve f(x) = a, solve f(x) = g(x), solve f(x) > g(x), etc.

1.2 Graph functions represented symbolically, numerically, or verbally:

1.2.1 Select the independent and dependent variables.

1.2.2 State plausible domain and range values of the function.

2.0 LINEAR FUNCTIONS
 The goal is to explore, analyze, and master linear functions.

2.1 Demonstrate the prerequisite skills of:

2.1.1  writing the equation of a line given two points or given a graph.
2.1.2  graphing linear functions using a variety of methods.

2.2 Solve applications in which students must find the equation of a linear function using y = mx + b and y - y1 = m(x - x1).

2.3  Construct new functions from functions represented graphically, symbolically, numerically and verbally.

2.3.1 Construct a composition of two linear functions.
2.3.2 Construct the inverse of a linear function.

2.4  Solve compound linear inequalities of one variable presented in symbolic form.

3.0 QUADRATIC FUNCTIONS
The goal is to explore, analyze, and master quadratic functions.

3.1  Demonstrate the prerequisite skills of:

3.1.1  graphing (by hand)  a quadratic function in standard form,

   f(x) = ax2 + bx + c, by identifying the axis of symmetry, vertex, horizontal, and vertical intercepts.

3.1.2  using the quadratic formula from memory.
3.1.3  solving quadratic equations using graphs, square roots, and factoring.

3.2  Solve quadratic equations for complex solutions.

3.2.1 Add, subtract, multiply complex numbers. 3.2.2 Conjugates and division of complex numbers and powers of i.
3.2.2   Distinguish between exact and approximate solutions of quadratic equations.

3.3   Explore quadratic functions in vertex form, f(x) = a( x - h) 2 +  k,.

3.3.1  Convert from standard form to vertex form by completing the square.
3.3.2  Investigate a, h, and k in terms of transformations.

3.4   Solve quadratic applications graphically and symbolically.

3.4.1 Applications to minimum and maximum problems.
3.4.2  Determine a reasonable domain and range.
3.4.3  All variables in applications shall be appropriately defined with units.
3.4.4  Interpret results and check for reasonableness.
3.4.5  Identify and solve equations that are quadratic in form
3.4.6  Given three non-collinear points, find the quadratic function passing through them algebraically,
3.5  Distinguish quadratic functions from other functions, given in symbolic and graphic form.

4.0 EXPONENTIAL FUNCTIONS
 The goal is to explore and analyze exponential functions.

4.1 Investigate exponential functions of the form:  f(t) = abt.
4.2  Preview the natural base e.
4.3 Graph exponential functions represented symbolically, numerically or verbally.
4.4 Generate tables for exponential functions represented graphically, verbally, or symbolically.  
4.5  Distinguish exponential functions from other functions given in symbolic and graphical form.
4.6  Match an exponential function given in symbolic form to its graph.
4.7  Find the exponential equation through two points.
4.8 Solve exponential applications graphically.

4.8.1 Determine a reasonable domain and range.  
4.8.2  All variables in applications shall be appropriately defined with units.
4.8.3  Explain, in context, the following geometric properties of an exponential function represented graphically, symbolically, numerically and verbally: Vertical intercept, asymptote, increasing and decreasing.

5.0 RATIONAL EXPRESSIONS AND EQUATIONS (INCLUDING COMPLEX FRACTIONS)
The goal is to algebraically manipulate rational expressions and to solve rational equations.

5.1  Simplify, multiply, and divide rational expressions.  
5.2  Add and subtract rational expressions.  
5.3  Simplify complex fractions.  
5.4  Solve rational equations.  
5.5  Applications to formulas, and modeling problems involving work and motion.

6.0 RADICAL EXPRESSIONS AND EQUATIONS
The goal is to algebraically manipulate radical expressions and to solve radical equations.

6.1  Find nth roots.
6.2  Explore the properties of rational exponents including the product rule, quotient rule and power rule.
6.3  Use the product rule to multiply and simplify radicals.  
6.4  Use the quotient rule to divide and simplify radicals.
6.5  Add and subtract radical expressions.  
6.6  Rationalize denominators and numerators.  
6.7 Solve radical equations.

7.0 TECHNOLOGY
The goal is to use technology to enhance understanding of concepts in this course.

7.1 Demonstrate the prerequisite skills of
7.1.1 entering equations in the y = menu  
7.1.2  setting domain, range, scale values, and using some zoom features
7.1.3  incorporating the graphing functionalities of
7.1.3a Zero/root  
7.1.3b fmax, fmin  
7.1.3c value/eval  
7.1.3d intersect
7.1.4 using the table feature
7.2 Use e for graphing and evaluating exponential functions.

7.3  Enter rational exponents.

 

          

 

The primary purpose of the Course Content and Outcome Guide is to provide faculty a SAC approved outline of the course. It is not intended to replace the Course Syllabus, which details course content and requirements for students.

This page is maintained by the PCC Curriculum office.
PCC © - An Affirmative Action, Equal Opportunity Institution.
by Curriculum 10/28/2003
















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