Quadratic Formula Derivation and Application to Penalty Kicks and Archery

In celebration of Maths Week London, University of Oxford mathematician Dr Tom Crawford derives the quadratic formula using the method of ‘completing the square’ and then applies it to solve real-world problems in football and archery.

We start with some examples demonstrating the method of ‘completing the square’ before using the technique to derive the quadratic formula. The equation is then used to solve the problem of calculating the perfect penalty placement in a game of football, and the motion of a projectile fired from high ground to a target below.

This is a special video to celebrate Maths Week London, June 28th – July 2nd 2021. Find out more here.

Watch Tom’s Maths Week London 2020 video on calculating the perimeter and area of the ‘Koch Snowflake Fractal’ here.