Algebra 2 · Grades 9 to 11
Quadratic equations
Solve quadratics by factoring and the quadratic formula.
The idea
A quadratic equation has the form ax² + bx + c = 0, where a is not zero. Its solutions are the x-values where the graph crosses the x-axis.
Factoring works when the expression splits into two brackets. The quadratic formula works for every quadratic equation.
Worked examples
- How to Solve a Quadratic Equation by Factoring Solve x^2 - 5x + 6 = 0 by factoring. Four steps, the zero-product reason, and the factoring mistakes that lose solutions.
- How to Use the Quadratic Formula Solve 2x^2 + 3x - 2 = 0 with the quadratic formula. Five steps, the discriminant, the sign mistakes to avoid and practice problems.
- How to Solve a Quadratic by Taking Square Roots Solve 2x^2 - 32 = 0 by isolating x squared and taking both roots. Four steps, the plus-or-minus sign, and the lost-solution mistake.
Practice this topic
4 problems with answers.