Alexa and I completed her last session by covering a variety of topics. We looked at polynomial functions, and talked about local max and min points, as well as where the x an y values increase and decrease.
We solved linear systems with substitution and elimination. Alexa remembered this from years ago.
We defined slope, slope-intercept from of an equation, and standard form of an equation. Alexa wrote equations in slope-intercept form, changed them into standard form, and wrote equations in point-slope form when given slope and a point. I think Alexa is ready for college!

We looked at the end behavior of polynomial functions. I made a chart for Alexa that broke down 4 situations, with even and odd exponents, as well as positive and negative leading coefficients. Alexa was able to look at polynomial graphs and determine the degree and sign of the leading coefficient. She was also able to look at polynomial functions and determine the end behavior of the graphs based on the degree and sign of the leading coefficient.

Alexa and I worked through logarithmic and exponential functions. We changed them back and forth in order to solve logarithms. We also expanded and condensed logarithms.

I spent some time showing Alexa how we account for subtracting and changing the signs when the distributive property is involved. I then re-explained the complex fraction problem from yesterday. We transitioned to solving rational equations. To do these, we must find the common denominator and multiply each term by it. This will allow the denominators to be eliminated, and we can solve the equations as linear or quadratic equations. Alexa has 6 more hours to complete!

Alexa and I talked about writing a reflection regarding her high school years. We discussed in depth her academic and acting career. We also talked about different ways to write about her final thoughts about high school. After much discussion, Alexa wrote a very nice paragraph which she titled "The Goodbye Paragraph."

Discuss in detail human population growth, factors which increase the growth and natural limiting factors which will slow down the growth or destroy the population.

Combine one of Alexa's mandala drawings with a portrait of herself using photoshop.

Alexa and I read and discussed three of Shakespeare's most popular sonnets. Sonnets 18, 30, 33 all deal with love and loss which fits nicely with the themes in the last two novels that Alexa has read. We discussed composing a Shakespearean sonnet. We looked at examples. We also discussed the writing of a senior reflection which Alexa has decided to write instead. She will compose a narrative of her early, middle and high school years as a senior reflection as she prepares to graduate.

Alexa and I continued working to reduce complex fractions with numerical and variable denominators. She likes to factor them and cancel the like factors. Tomorrow we will review the idea of negatives more, as they can be tricky with these operations.

human population growth and the effects on the biosphere