The second volume of this series ignites a passion for mathematics, specifically for the kind of mathematics that, like elementary geometry in the first volume, has long shaped school education. Readers can take a brief look at the 4000-year history of quadratic equations and discover their connection to the geometry of conic sections. Additionally, they will learn about applications of conic sections in physics and astronomy and uncover how powerful even elementary mathematics can be when taken seriously. The final chapter goes slightly beyond classical school mathematics and demonstrates how the algebra and geometry of conic sections provide a new approach to a well-known Olympiad problem from number theory. The same author has previously published in the series: Mathematics à la Carte - Elementary Geometry at Square Roots with some g.