9-6 the Quadratic Formula and the Discriminant – We learned that the discriminant of a polynomial is a quantity that depends on the coefficients and determines various properties of the roots. It is generally defined as a polynomial function of the coefficients of the original polynomial. We learned that the quadratic formula can be used to solve every quadratic equation and is particularly useful for those that cannot be easily factored. Then we learned to use the discriminant to determine the number and type of solutions to a quadratic equation. Next we began to review for an end-of-course cumulative exam.
Ben said he had a stomach ache this morning. I encouraged him to push past it and work with me. He did but was distracted. We worked on exponent properties, a concept we've spent a lot of time on. I gave him an activity with basic problems to see if he could recall the properties. He struggled a bit, but with help was able to use what he learned from one problem to simplify the next. I wrote out the rules again so he could see why we add powers when multiplying and multiply powers when we have a power raised to a power.
Instead of having a traditional math class, today we worked on puzzles, riddles, and logic. I showed Ben pictures of multiple squares and asked him to count how many he saw. He realized that multiple squares could be created beyond what is obvious. Next we considered riddles regarding age and probabilities. We also looked at photos that initially you see one way, but when you look at it again with a different perspective you can see something different.
9-4 Solving Quadratic Equations Using Square Roots – We learned that when the quadratic equation is in the form ax2 + bx = c, it can be solved by isolating the ax2 term, simplifying to remove the coefficients, and then taking the square root of each side of the equation. We practiced several of these type of problems where we take the square root and have two possible solutions. Next we reviewed completing the square to find the answers to a quadratic equation that is not able to be factored.
Assignment: Complete the assigned problems for homework.
9-5 Completing the Square – We learned to complete the square by adding the square of half of the coefficient of the x to each side of the equation. Then we solved quadratic trinomials by completing the Square to what completing the Square to write a quadratic equation in Vertex form.
