Grade 10s patterning continues

We worked on this pattern today

We saw things in so many ways!

We made a lot of equations which all simplified to the same thing.

The next step was to make a graph.  The trick was it’s not a factorable equation.  We needed a new step to find the vertex (le sommet).

We looked at some perfect squares (we’ve done lots of practice with these).  We know they have one root (racine) and it is also the vertex (sommet).  What happens if there is a constant at the end, after the perfect square.  It turns out that if the bracket turns to zero, the final number will be the minimum value of the parabola (part of the vertex).

We got good at that, so we tried to make a perfect square out of our expression

We used algebra tiles, splitting the 8x up into 2 groups of 4x and then we needed 16 squares to complete the square.  We already had 4, but we needed 12 more.  We added 12 zero pairs (blue and red squares together) so now we have a full square, and 12 blue squares left over 

Our equation is y=(x+4)^2-12 and from this we know that the vertex (sommet) is (-4,-12).

We then looked at calculating the roots (racines) by setting y to 0 and then solving for x by using opposite operations.  We’ll do more practice with this next week.