# Pre-Calculus Chapter 2 Essential Questions

For Chapter two I have devised a summary for my students to complete. Below are the Essential questions I am asking my students to review and make sure they understand. I will have them insert their summary to the comment section below.

**Directions: **For your summary you will choose to answer some of the questions outlined below in a logical format to bring together what you have learned for this Unit. In is important to answer the questions and connect them in a format that describes in your view what you have taken from this unit. At the end of the summary you may also bring up additional questions that you still need answered or clarified. The summary is your interpretation of the material from the unit and should not be based on other student or book answers.

**Essential Questions: **Answer the following in a summary for what you have learned for the given information.

**2.1 – **

What is the main characteristic between a quadratic and other polynomials?

Why do all parabolas have an axis of symmetry? **
** Is it possible to have more than one vertex explain?

What are the three types of solutions to a quadratic graph?

What does –b/2a represent?

Are all quadratics symmetric?

What is the importance of vertex form compared to standard form?

Why does the vertex of a quadratic tell you?

**2.2-**

What is the definition of a polynomial?

What are examples of non continuous functions?

What is the leading coefficient test and how can we apply it?

How are a solution, factor, zero and intercept of a polynomial related?

What are the benefits to knowing how to graph polynomial functions?

Why is the intermediate value theorem useful?

When do you have repeated zeros with multiplicity?

How can we determine the zeros of a polynomial?

What does the number of zeros tell us about a polynomial?

How does the number of turning points relate to the degree of a polynomial?

How does the number of zeros relate to the degree of a polynomial?

How can we determine the domain and range of a continuous polynomial with even degree?

How can we determine the domain and range of a continuous polynomial with odd degree?

How do you utilize polynomials to determine a maximum or minimum in real world situations?

Why is it helpful to understand the fundamental theorem of algebra and linear factorization theorem?

**2.3-**

What does division of polynomials tell us?

What is the division algorithm and it’s parts?

How is it useful to know the remainder of a quotient, what does it tell you about a polynomial? It’s factors zeros and intercepts?

If a binomial divides evenly into a polynomial, what does that say about the binomial as a factor and zero?

How do we set up the synthetic division algorithm and apply it?

How are the remainder and factor theorem related?

What does the remainder in synthetic division tell us about the polynomial, factors and zeros?

What does it mean for a divisor to evenly divide into a dividend?

How can you check polynomial division?

**2.4-**

What is the definition of a complex number?

What is the definition of the imaginary unit?

What is the definition of an imaginary number?

What is and the parts of the standard form of a complex number?

For complex numbers to be equal what parts must also be equal?

How are the operations of complex numbers related to the operations of real numbers?

How are the operations of complex numbers different to the operations of real numbers?

Show that the multiplication rule of imaginary numbers repeats?

When dividing complex numbers how will we apply the operation differently when the denominator is pure imaginary and complex?

What does the principal square root help us do?

When do we have complex solutions to a quadratic equation?

**2.5-**

What is the Descartes rule of signs?

Why is it helpful to know the upper and lower bound rules as well as Descartes rule of signs?

What is the rational zero test and it’s parts?

What does the fundamental theorem of Algebra tell us about all polynomials?

What does the linear factorization theorem tell us about how we can write a polynomial?

Given the rational zero test how can we test the possible zeros of the polynomial?

When and how are complex conjugates and conjugate pairs applied?

What do conjugate pairs tell us about the zeros of a polynomial?

How does Descartes rule of signs defer from the rational zero test?

**2.6-**

What happens when the denominator of a rational function is 0?

What are asymptotes?

How can you graph a rational function?

What are asymptotes and how do we find vertical, horizontal and oblique asymptotes?**
**What makes up a rational function?

How do vertical, horizontal and oblique asymptotes affect our domain and range?

How do we find the x and y intercept of a rational function?

How we test for symmetry of a rational function?

What is the horizontal asymptote test?