Why this chapter matters
Quadratics model area, projectile motion, and optimization while introducing equations that can have two, one, or no real solutions.
What you will learn
- Choose an efficient method for solving a quadratic equation.
- Use the discriminant to predict the number of real solutions.
- Interpret roots, vertex, axis of symmetry, and intercepts on a graph.
Lessons in this chapter
- Solving by factoringUse the zero-product property after putting the equation in standard form.
- Completing the squareRewrite a quadratic in vertex form.
- The quadratic formulaSolve any quadratic and interpret the discriminant. Read the full guide →
- Graphing parabolasConnect algebraic forms to roots and vertex behavior.
Study task
Model the height of a thrown object with a quadratic, identify its maximum height, and find when it returns to the ground.
Chapter checkpoint
Solve x^2 - 5x + 6 = 0.
Factor as (x - 2)(x - 3) = 0, so the solutions are x = 2 and x = 3.