Cal and I worked on using the quadratic formula to solve problems related to quadratic equations. We discussed the use the quadratic equation to find solutions for x that satisfy a quadratic equation when y = 0. This information is vital to factoring quadratic and trinomial equations. Cal worked through several problems to factor equations and find an axis of symmetry for an equation.

We started out with the jailing of four Blackwater contractors.

Today, Cal and I reviewed the use of the quadratic equation to plot functions with curved lines. We discussed using factoring to break down the quadratic equations and find the solutions for x when the equation is set to have y = 0. Cal worked through plotting several quadratic equations, and I was able to explain the impact of the multipliers in front of the squared term for x. Additionally, we looked at the uses of the quadratic formula to assist in factoring quadratic equations.

We explored both campaigns and their opening salvos. The comparison was very interesting. We wondered if trends on social media are reflected in actual elections.

Today, Cal and I discussed the nomenclature for functions containing more than one variable. We discussed the difference between the dependent variable, y, and the independent variable, x. Cal and I worked through several problems using the vertical line test to determine if a line is a function that results in only one answer for y for each value of x. Cal also learned the meaning of domain and range as related to functions with variables x and y. We also briefly discussed the use of ratios in math, chemistry, cooking, and engineering.

Cal and I worked on understanding exponents and exponential functions. It was important for me to reiterate the Cal the use of a function in math and how the symbols used to express a function can be interchanged without impacting the math for the function. We worked through problems related to both exponential growth and exponential decay. Cal also read through the beginning of Chapter 9 on the difference between a monomial and a polynomial expression. We worked mainly graphing several linear binomial equations, however Cal was also introduced to the graphical expressions resulting from trinomial equations such as a quadratic equation. Toward the end of the time, Cal worked to graph an exponential equation in x-y- coordinates.

We discussed Cal's project on John Hancock and decided to do some internet research on him. We found, among other things, that besides his famous signature on the Declaration of Independence, Hancock had been very wealthy, a smuggler and attended the coronation of King George III. On top of that, he was very much an American patriot. I suggested that a poster might be the way to go. We were able to compile a fair amount of notes.

Today we worked on solving systems of linear eqautions. We also discussed the use of exponents including negative exponents and fractional exponents (i.e. square roots, cube roots, etc.). Cal and I discussed some of the uses of solving linear systems of equations.

We are examining both the historical period and the specific issues that we need to address for the assignment he has been given.

We went over the basics of historical essay writing in terms of structure since that is what Cal is studying at school in English class, an integrated approach to teaching English and History.