"Math Maven: Empowering Exploration, One Equation at a Time!"

Kaylah is teaching a student ("cookie dough") about polynomial end behavior and simplification. She explains how the leading coefficient and exponent determine end behavior, emphasizing the importance of simplifying like terms and memorizing the rules. She plans to provide further practice on these concepts.

Kaylah and Cookie Dough had an online lesson where Kaylah, after apologizing for being late and rescheduling their next meeting, explained quadratic functions and polynomials. She used Geogebra to demonstrate how the coefficients A, B, and C in the quadratic equation y = ax² + bx + c affect the parabola's shape and position. She covered roots, standard vs. vertex form, and factoring for finding roots. She then introduced polynomials, emphasizing the importance of the leading term and coefficient, and stated the next session would delve deeper into polynomial rules.

Kaylah tutored Cookie Dough, guiding her through logarithm and quadratic equation problems in preparation for the Illinois Institute of Technology's Computer Science ALEKS placement exam. They reviewed techniques for manipulating logarithmic expressions and applying the quadratic formula. The next session is scheduled to cover exponents, polynomials, and roots, focusing on rewriting expressions and mastering fundamental rules.

Kaylah tutors "cookie dough" on solving logarithmic equations. They work through problems involving combining logs, exponentiating, and factoring, including those with natural logs (ln). Kaylah then demonstrates two methods to solve 2log₂(x) = 3 + log₂(x-2): one using the quotient rule and the other converting the constant to a logarithmic expression. Both methods lead to the solution x=4, and Kaylah stresses understanding logarithmic rules and relationships.

Kaylah tutored Cookie Dough on solving logarithmic and quadratic equations. She covered combining logarithms (addition becomes multiplication, subtraction becomes division), exponentiating to remove logs, using the quadratic formula, simplifying radicals, and eliminating fractions by multiplying by the denominator. A key point is checking solutions to ensure they don't make the original denominator zero in fractional equations, as this would invalidate the solution.

Kaylah tutors "cookie dough" on exponents and logarithms, reviewing rules, properties, and problem-solving techniques. She demonstrates solving logarithmic equations using methods like equating the inside of the log to 1 and exponentiating with the base, emphasizing natural logs and logs with different bases. They work through examples, including using the quadratic formula, and Kaylah clarifies the process of exponentiating to eliminate logarithms. They plan to continue practicing logs before moving on to polynomials.