Patterning to Graphing

Grade 10s continued to work on their patterning activity from a few days ago.

We had previously constructed and graphed the pattern.

But now we are working on figuring out an equation to model the situation.

We are working from the visual representation, and connecting what we know about the graph from the tables of values.  We know the “a” value is half of the second differences, and we know that in this case figure 0 is 0, so our constant is 0.

Some of us are working on simplifying complex equations…
If we use the colours as a way to group things….

We get a long equation!

If we ignore the colour…

We get a simpler equation

If we are creative and try to rearrange the circles…

We can create rectangles that have dimensions 2x and (x+1) so that leads us to a simple equation! Y=(2x)(x+1)

Here’s another way to factor that expression

Working from our table of values we can determine the a and c values…

We can substitute any point as x and y and calculate b, and then we can factor, determine the roots, and then the vertex (sommet), and draw the graph.

This is the next one we are working on: here are figures 1-4