Day 155: Graphing

Today was rough.

Algebra is just getting into solving quadratic equations. We looked first looked at solving linear equations like 3x + 4 = 10 and talked about how these were solved and what was happening to x in equation.

After a while I threw up x² + 4x = -3.

Students tried to solve it by moving the 4x over and were frustrated that they couldn’t get the equation down to just one x. They whole group divided and conquered on different values of x, and eventually they reached two solutions.This took a lot of time, time students don’t have, they asked for a better way.

Then I messed everything up.

No matter how I modified the lesson between periods, students struggle with the process of setting the equation equal to 0, graphing the related function, heading back to the equation to remember they were looking for x-values that produced y-values of 0, then using the graph to help them.

Too much.

I had blank stares all day, something is wrong on my end. Maybe I haven’t emphasized WHY graphs are useful, but, we talked a lot about how graphs generate y-values based on chosen x-values. This is almost the same thing.

I also probably shouldn’t have made them suffer by graphing each equation by hand…

Let me know below how you navigate into solving equations by graphing.

To get students into the swing of comparing 2-4 quadratic functions I had them pick up an equation and graph on their way in today. The equations were of the form y = ax² + c, and either had different a values or c.

They put ’em up by colors and had a quick galley walk, discussing the similarities and differences.

Desmos and the ability to add sliders, made everyone’s lives a whole lot easier when it came down to comparing functions like:

f(x) = x²

to

g(x) = -¾x² – 12.

Students seemed to pick up on transformations pretty quick and did well in describing the differences between functions.