Students will learn what the quadratic formula is and how to use it to factor and solve quadratics. They'll also learn how to derive it by completing the square. Here's a video covering the derivation. When asking students to solve quadratics using the quadratic formula, don't just ask them to solve equations like \(ax^2 + bx + c = 0,\) but also variations, such as \(bx + ax^2 = c.\) Next, give your students this challenge: Find the value of \(x\) (video):

$$x = 1 + \dfrac{1}{1 + \dfrac{1}{1 + \dfrac{1}{1 + \ldots}}}$$Lastly, give your students this challenge.

Conclude by giving your students these challenges:

- Trebling by NRICH
- Jig Shapes by NRICH
- Sweeping Hands by NRICH
- 2012 AMC 8, Problem 11
- 2016 AMC 8, Problem 10
- Game, Set, Match by Pierce School: Problem / Solution