Skip to content

References: Quadratic Functions and Equations

  1. Quadratic function - Wikipedia - Comprehensive article covering the properties of quadratic functions, including standard and vertex forms, parabola graphs, vertex, axis of symmetry, and maximum/minimum values discussed throughout this chapter.

  2. Quadratic equation - Wikipedia - Detailed overview of quadratic equations, including solution methods (factoring, completing the square, the quadratic formula), the discriminant, and the nature of real and complex roots.

  3. Quadratic formula - Wikipedia - In-depth explanation of the quadratic formula's derivation from completing the square, its use in solving any quadratic equation, and its relationship to the discriminant.

  4. Larson, Ron and Laurie Boswell. Big Ideas Math: Algebra 1. Big Ideas Learning, 2019. - A widely used Algebra 1 textbook with a full chapter on quadratic functions and equations covering graphing, factoring, completing the square, and the quadratic formula.

  5. Charles, Randall I. Prentice Hall Algebra 1. Pearson, 2015. - Standard Algebra 1 textbook that presents quadratic functions, parabola graphing, and all major solution methods for quadratic equations with extensive practice problems.

  6. Solving Quadratic Equations by Factoring - Purplemath - Step-by-step lesson on solving quadratics by factoring using the zero-product property, with worked examples and common student mistakes, directly supporting the factoring method taught in this chapter.

  7. Completing the Square - Math Is Fun - Clear walkthrough of the completing-the-square process, transforming ax² + bx + c into a(x + d)² + e form, matching the step-by-step method presented in this chapter.

  8. The Quadratic Formula - Math Is Fun - Explains the quadratic formula, standard form, and the discriminant's role in determining real, repeated, or complex solutions, reinforcing the formula and discriminant sections of this chapter.

  9. Axis of Symmetry of a Parabola - Mathwords - Reference page defining the axis of symmetry formula x = -b/(2a) with worked examples from both standard and vertex form, supporting the graphing and vertex sections of this chapter.

  10. Imaginary Numbers - Math Is Fun - Introduction to the imaginary unit i and complex numbers, showing how they arise when solving quadratics with negative discriminants, connecting to the complex number section of this chapter.