Using given zeros to find the remaining zeros in a polynomial by dividing out the known factor. Factoring using the "ac" method and the quadratic formula - Find all rational zeros using the rational zeros theorem and synthetic division.
Definition of quadratic functions - Examples. Expression in standard and vertex forms - The parabola - Transformation by stretching and shifting vertically and horizontally - Conversion from standard form to vertex form by completing the square - Writing quadratic equations for given parabolas -
Josh and I reviewed a number of different problems in a packet in order to prepare him for his final exam. There were problems from many topics including equations of lines, exponential functions, and natural logarithms. Josh stated that he had to score very well on the final exam in order to pass the course with a 'C'. There was no assignment.
Assignment
See lesson outline.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Joshua works hard but has not been successful on his tests.
Joshua showed me his work on one-to-one functions and finding inverses of functions. We worked on the skill of identifying the graphs of exponential functions. Then I showed him how to raise a number to a rational root and how to solve equations between two different bases raised to variable expressions as their powers. There was no assignment.
Assignment
See lesson outline.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Joshua worked hard in advance of our session and was fully prepared to understand the work we did together.
Joshua brought in a work packet containing mostly multiple choice questions. Many of the questions required him to choose which equation matched which graphs. He correctly identified most of them. He was also tasked with creating polynomials given their zeros. There were many pages of problems but Joshua was able to finish the problems and check his work against the answer key. He got most of them correct. There was no assignment.
Assignment
See lesson outline.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Joshua has worked hard on this material and has a strong probability of doing well on the test next week.
Quadratic maxima or minima, verices of parabolas, polynomial solutions
Lesson Outline
Josh and I worked several problems to determine the vertex, axis if symmetry, domain, and range of quadratic functions. We then studied synthetic division, zeros of polynomials, and the use of several theorems to determine divisors.
There was no assignment.
Assignment
See lessson outline.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Joshua comes to our lessons prepared with questions he needs to ask which saves time.
Domains of functions and solving systems of linear equations
Lesson Outline
Josh needed help studying for a test that he's taking on Monday. He needed to understand how to find the domain of functions which have variables in the denominator of a fraction or inside a square root. I showed him how to write the domain in interval notation.
We then worked on solving some linear systems by the substitution and elimination methods. There was no assignment.
