QR - Quadratics Revisited Module Overview

Math_AdvAlgConceptsConnectBanner.png Quadratics Revisited Module Overview

Introduction

In mathematics, a  Polynomial  is an expression consisting of variables and coefficients. Polynomial expressions have the following operations: addition, subtraction, multiplication, division, and non-negative integer exponents. 

Polynomials have many applications; here are a few of the applications:

1. Finding displacement of objects in Newtonian mechanics, such as how fast or slow it takes an object to fall from a given height, whether it is thrown or dropped. The optimal arch of a basketball as someone shoots it toward the rim. How long, what velocity, and what arch a quarterback needs to throw a football to a receiver.

2. Economists use polynomials to represent cost functions, and they also use them to interpret and forecast market trends. Statisticians use mathematical models, where polynomials are used to analyze and interpret data, as well as draw conclusions from the data. Financial planners use polynomials to calculate interest rate problems to determine how much money a person needs to accumulate over a given amount of time with a specified initial investment.

3. In meteorology, polynomials are used to create mathematical models that represent weather patterns that can be analyzed to make weather predictions.

4. Engineers that design roller coasters use polynomials to describe the various curves in the rides.

Quadratic Equations and Inequalities are a part of the Polynomials family. Quadratic Equations and Inequalities introduce students to the graphs of quadratics, teaches them to find the vertex, intercepts, discriminant, domain and range and interpret the graph in relation to these qualities.

Essential Questions

  • How are rational exponents defined?
  • How are expressions involving radicals and rational exponents rewritten?
  • How is the imaginary number i defined?
  • How are complex numbers defined?
  • What are the rules for complex numbers operations?
  • What is a quadratic function?
  • What are the rules for graphing quadratic functions?
  • What are the characteristics of a quadratic graph and how are they represented?
  • How are rational exponents defined?
  • How are expressions involving radicals and rational exponents rewritten?

Quadratics Revisited Key Terms

Polynomial - The sum or difference of two or more monomials.

Constant - A term with degree 0 (a number alone, with no variable).

Monomial - An algebraic expression that is a constant, a variable, or a product of a constant and one or more variables (also called "terms").

Binomial - The sum or difference of two monomials.

Trinomial - The sum or difference of three monomials.

Integers - Positive, negative and zero whole numbers (no fractions or decimals).

Like Terms - Terms having the exact same variable(s) and exponent(s).

Coefficient - Number factor; number in front of the variable.

Imaginary Number - A number that involves i which is 

Complex Number - A number with both a real and an imaginary part, in the form a + bi

Conjugate - The same binomial expression with the opposite sign.

Greatest Common Factor - Largest expression that will go into the terms evenly.

Zeros - The roots of a function, also called solutions or x-intercepts.

Linear - A 1st power polynomial.

Quadratic - A 2nd power polynomial.

Cubic - A 3rd power polynomial.

Quartic - A 4th power polynomial.

Intercepts - Points where a graph crosses an axis.

System of Equations - n equations with n variables.

Point of Intersection - The point(s) where the graphs cross.

Consistent - Has at least one solution.

Inconsistent - Has no solution.

Domain - The values for the x-variable.

Range - The values for the y-variable.

Extrema - Maximums and minimums of a graph.

Rational Exponent - A rational number written in the exponent of the form , where a is the base of the exponent, m is the numerator (power), and n is the denominator (root of the radical).

Math_OverviewBottomBanner.png IMAGES CREATED BY GAVS