Memorizing the exact formula of the Quadratic equation may not be necessary - knowing that the quadratic equation exists and what it is does is the useful part. Even more useful is to recognize a problem and realize the quadratic equation applies to it.
Trigonometry or calculus are better examples of this. Memorizing every formula and then promptly forgetting about them 5 minutes after passing the test is not useful but learning the concepts and the fundamentals and how they apply to solving a whole slew of problems is the useful part. Algebra is extremely abstract (especially if you are a school pupil - "I'll never use this in the real world") but understanding it unlocks a whole lot of higher level conceptual ways of thinking and approaching problem solving.
You'll have far better success using a calculator (or chat GPT or Wikipedia) if you know not just what to punch into it by the why as well.