## Is this a thing?

• It has been far too long ago since I last learned mathematics in a high school setting, but the concept of learning through explorative/deductive strategies versus rote memorization is very popular at current times.

21°
• Paywalled.
Can someone with access to the article, summarize shat the trick is ?

26°
• >>26
"This alternate method for solving quadratic equations uses the fact that parabolas are symmetrical.

For example, in this parabola:

y = x^2 – 4x – 5

The two solutions when y = 0 are the symmetrical points r and s, where the parabola crosses the x-axis.

The midpoint, or average, of r and s is the axis of symmetry of the parabola. We want r + s = –b, which happens when the average of r and s is –b ÷ 2. In this example: 4 ÷ 2 = 2.

The two solutions to the quadratic equation will be the axis of symmetry plus or minus an unknown amount, which we’ll call u. In this example:

r = 2 – u and s = 2 + u

To find u, we want the product of r and s to be equal to c, which in this example is –5. Rewriting r and s in terms of u:

r × s = –5

(2 – u) × (2 + u) = –5

Solving that yields 22 – u2 = –5 or u2 = 9, so u = 3 works.

The two solutions to this quadratic equation are 2 – u and 2 + u, or –1 and 5. In other words, this parabola intersects the x-axis when x = –1 and x = 5."

28°
• >>28
>Solving that yields 22 – u2 = –5 or u2 = 9, so u = 3 works.
Solving that yields 22 – u^2 = –5 or u^2 = 9, so u = 3 works.

Sorry. Copy-and-paste mistake.

29°