Algebra 1 · Chapter 7 of 8

Quadratic Equations and Graphs

Solve quadratic equations by factoring, square roots, completing the square, and the quadratic formula, then connect solutions to a parabola.

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

  1. Solving by factoringUse the zero-product property after putting the equation in standard form.
  2. Completing the squareRewrite a quadratic in vertex form.
  3. The quadratic formulaSolve any quadratic and interpret the discriminant. Read the full guide →
  4. 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.