[Tainnor]

I guess then the point becomes - in the age of computers, what's the value in memorising the quadratic formula without understanding where it comes from?

It's much more important to know that there is a quadratic formula, or more fundamentally that every quadratic equation has 0-2 roots (exactly 2 if dealing with complex numbers) and what the different cases loom like (does the parabola touch or intersect the x-axis?). It's typically more important to be able to solve a quadratic equation through guessing, factoring or completing the square. Because these things teach you something about how mathematics works, regurgitating some formula serves no purpose, you can just ask Wolfram|Alpha instead. And even if you can't complete the square etc., I'd much rather people understood the conceptual side of it instead of remembering formulas.

[ntsplnkv2]

I don't think it has anything to do with computers. Tests have had formula sheets for decades, the quadratic formula would typically be on there.

The importance has always been "how its applied." Tons of people failed classes despite knowing the formula. It has always been about the basic application.

I don't think many math tests consisted of "write down the quadratic formula" and that's it.

[Tainnor]

The point is more that before computers, you could at least make a somewhat reasonable claim that it's useful to know the formula in case you need to solve a quadratic - even if you don't understand the formula.

But nowadays, you can just feed the equation to Wolfram|Alpha (or Sage, or Mathematica, ...), so there is no point in blindly memorising formulas.

And I don't think I've ever had a formula sheet in one of my maths exams in school...