How To Execute The Quadratic Equation Magic Trick?

If you are into math tricks, you will love this one!

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The quadratic equation magic trick is not your usual run-of-the-mill math trick. It raises the bar a couple of notches. Usually, mathematical magic tricks start with you asking someone to think of a number in their head. In this case, you ask them to think of an entire formula in their head.

The only requirement you impose is that it has to be a quadrating formula (an equation which features its highest variable power as x²). Following this, you ask them to work out the output value of the formula for following inputs: x = 0, x = 1, and x = 2.

Once the person reveals the respective output values to you (not the formula), you think for a moment, and then reveal the equation that the person had originally thought of. That is the trick!

In this essay, I will first cover how you can execute this trick. Then, I will explain why the trick works and touch upon the deeper mathematical principle that enables this trick. Let us begin.

How to Execute the Quadratic Equation Magic Trick

Let us first assume that the person playing the game with you has chosen the following equation in their head: