Visual patterns

we’re practicing how to make equations from visual patterns in grade 10. We are using colours to show different terms. In this we have 2 n by n squares, and 3 groups of n in each figure. We see figure 1,2,3 shown.we can make tables of values and show that our pattern is growing quadratically, since the second differences are the same.sometimes there are a few ways to view a pattern, and we can make different equations (that would all simplify to the same thing in the end)we looked at how to find the vertex of this equation. We decided to complete the square just to see if we could, even though the numbers are not so friendly. We use the same visual method, and use fractions or decimals.

We could also have used the quadratic formula to find the roots, then found the axis of symmetry and then the vertex. It’s great there are so many options!