Deriving the Quadratic Formula — Practice Companion
Now that you've derived the formula by completing the square, this is where you build fluency — both in using it and in understanding why it works. Take your time. Get stuck if you need to — getting stuck is part of the work. There are four kinds of help on every question: a Socratic question (which asks you something rather than telling you), a hint (which gives you a piece of the method), the answer check (which you can use as many times as you like), and a worked solution (which unlocks once you've had a genuine go).
Well done — you've worked through every question. 🌱
Take a moment for the reflection below. You can also press Ctrl+P (or ⌘+P) to print or save your work, including all the reveals and your written workings.
💛 Reflection
Mirroring the Living Body panel of the lesson: how did that feel? There are no wrong answers — these prompts are just to notice what's happening.
- Which felt more secure — using the formula, or explaining why it works? What might that tell you?
- Did any question change how you think about the formula you've used so many times before?
- When you applied the formula, did you find yourself trusting it more now that you've derived it?
- On a scale of 1 (still feels like magic) to 5 (I could rebuild it from scratch), where are you now with the quadratic formula?