Why completing the square is the ultimate shortcut for graphing quadratics
In short: While factorising and the quadratic formula are standard tools, completing the square offers a unique geometric advantage. This video demonstrates how to transform a quadratic equation into a format that instantly reveals its most critical features.
Completing the square is a universal method for solving quadratics, unlike factorising which can fail depending on the numbers involved. By rearranging the equation into the form (x - a)² + b = 0, you can immediately identify the coordinates of the turning point (a, b), which represents the maximum or minimum of the graph.
This technique provides four essential points for sketching a quadratic: the turning point, the y-intercept (found in the original equation), and the x-intercepts (found by solving the completed square). It serves as a comprehensive roadmap for visualizing the curve's behavior.
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Sources
- Summary by Intellect · source: Completing The Square - Plotting Quadratics | Algebra | Maths | FuseSchool
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