Complete the Square and Vieta's Formulas | Six Minutes: Waterloo Fermat Contest, Part 6

Six Minutes: Waterloo Fermat Contest, Part 6: Complete the Square and Vieta's Formulas: Vertex and max/min without graphing; then Vieta's Formulas Completing the square rewrites any quadratic as a square plus a constant, so the vertex and the maximum or minimum value fall out with no graphing. This episode gives the recipe, a worked minimum found two ways, and the factored-coefficient trap. Then: Vieta's formulas give the sum and product of a polynomial's roots straight from its coefficients, with no solving. We use them to find expressions in the roots fast, rebuild quadratics, and avoid the classic sign trap. Chapters 0:00 Introduction 0:21 The idea 0:43 The recipe 1:04 Worked example 2:03 The trap 2:23 Recap 2:51 The idea 3:24 Why it wins time 3:58 Worked example 4:35 Trap 5:00 Recap 5:15 Thanks for watching Practice problems 1. Find the minimum value of x^2 - 10x + 3. (Answer: -22, at x = 5.) 2. Find the maximum value of -3x^2 + 6x + 4. (Answer: 7, at x = 1.) 3. The roots of x^2 - 9x + 18 = 0 are r and s. Find r^2 + s^2. (Answer: 45, since r + s = 9 and rs = 18, so 81 - 36 = 45.) 4. Two numbers have sum 6 and product 7. Find the sum of their reciprocals. (Answer: 6/7, since 1/r + 1/s = (r + s)/rs.) Six Minutes @SixMinuteClass: One technique, about six minutes. The narrator's voice is synthetic (computer-generated). Independent educational video. Not affiliated with or endorsed by the Centre for Education in Mathematics and Computing (CEMC) or the University of Waterloo. © 2026 Six Minutes · @SixMinuteClass