Students will learn how to determine the number of real roots for quadratics in factored form, standard form, and vertex form. For practice, give your students these problems, then this one.
Concude by giving your students this challenge:
Find the total area, that of all the green squares:
Here's the solution: Look at the squares from right to left. Call their side lengths \(s,\) \(s + 8,\) and \(s + 5,\) respectively. Thus, \(s + (s + 8) + (s + 5) = 25.\) Solving for \(s,\) we find \(s = 4.\) The area of all the squares must be \(s^2 + (s + 8)^2 + (s + 5)^2 = 4^2 + 12^2 + 9^2.\) Finally, evaluating the right-hand side gives us \(16 + 144 + 81 = 160 + 81 = 241.\)