Day 1
- Replay Polygraph on Desmos with improved vocabulary -- try to focus on precise descriptions of the graphs to quickly eliminate the ones that don't fit.
- Class practice describing graphs
- Practice finding the equation for the following set of points
x y 0 14 1 6 2 0
Friday's quiz will cover finding the equation for a given set of points. Some of them will be linear, some will be quadratic. I encourage you to use the method of plugging in values to the general form of the equation, either \(y = mx+ b\) or \(y=ax^2 + bx + c\) as this will give you a system of equations to solve for the coefficients, which we have practiced a lot at this point.
- Graph the following equation in Desmos \(y = 5x^2 + 2x - 10\), by choosing x values, plugging them into the equation to generate the y-values that match, then putting them into a table. Finally check the result using the equation entry.
Day 2
- Practice finding quadratic from data
- Review vocabulary. I'm not, in general, big into memorizing vocabulary, because I think it can distract from understanding meaning by focusing on a particular definition. But it is useful to have specific words to refer to specific things. So a good way to practice vocabulary is to attempt to describe a thing, like "the scoopy thing starts on the right side of the graph", and then to learn words that make it easier to be precise, like "the vertex is in the fourth quadrant".
- The data below comes from measuring the distance a car travels after slamming the brakes, at different speeds (It takes longer to stop if you are travelling faster). Attempt to find a line that fits with this data, as well as possible; then attempt to find a quadratic that fits with this data, as well as possible.
Which equation fits better? Why?
What does the x-intercept and y-intercept for each equation mean? Do they make sense?
Day 3
- Transformations of linear equations. We're at a point where we need to start thinking about equations and their graphs in a more sophisticated way -- we need better vocabulary and better conceptual tools for understanding what is going on with the different pieces of an equation. This will help us in a couple of ways: it will make it easier to use equations to model more complicated situations, and it will enable us to handle learning new domains a little faster and a little better. So we're going to explore a bunch of equations of lines and talk about what the differences in the equations mean for their graphs. We'll then extend this discussion into quadratic equations and graphs next week.
- The graph here on Desmos has a bunch of equations for lines in the data entry section, but none of them are displayed. Taking them one at a time, I want you to look at the equation, then draw on paper what you predict the graph will look like, then click the button next to the equation to display it to compare with your drawing. If you are unsure how to start, make a table of x and y values that fit the equation, like:
x y 0 0 1 1 2 2
which is the table for the first equation in the linked graph, \(y = x\).
Day 4
- Quiz on finding the equations for data. Some will be linear, some will be quadratic
Is something unclear? Leave a comment below:
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