Modelling quadratics

Grade 10s are working on solving problems involving quadratics.  This example shows how we can determine dimensions of a rectangle given the area and perimeter.  We can create equations, substitute, expand to make a trinomial, use algebra to get a trinomial that equals zero, and then use the quadratic formula to solve for the roots (if they exist).

We also saw that sometimes there are no roots.  In this case on desmos we can see that there are no intersection points between our two equations, so we have no possible dimensions that will work.  It corresponds to the fact that the discriminant found is a negative number.

Our work this week is mostly based on modelling (creating equations) and using them to solve problems.