Quadratic Equations
Factoring, the quadratic formula, completing the square, and graphing parabolas.
This page is a free outline of what the Quadratic Equations lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Completing the Square Completing the square rewrites a quadratic as a perfect square you can solve by taking a square root — add the square of half the middle coefficient to both sides to form (x + b/2)².
- Discriminant The discriminant, b² − 4ac, tells you how many real solutions a quadratic has: positive means two, zero means one, negative means none — without solving it.
- Evaluating Expressions To evaluate an expression, substitute a number for each variable and compute using order of operations. Evaluating 3x + 5 at x = 4 gives 3(4) + 5 = 17.
- FOIL (Multiplying Binomials)
- Graphing Parabolas The graph of a quadratic is a U-shaped parabola. It opens up when a > 0 (a minimum) or down when a < 0 (a maximum), with its turning point called the vertex.
- Parts of an Algebraic Expression An expression is built from terms separated by + or − signs. Each term has a coefficient (the number) and usually a variable (the letter); a constant is a fixed number. In 7x + 3, 7 is the coefficient, x the variable, 3 the constant.
- Quadratic Equations – Identifying & Standard Form A quadratic equation has an x² term and none higher; its standard form is ax² + bx + c = 0. Solving it means finding the x-values (roots) where the parabola crosses the x-axis.
- Quadratic Word Problems A quadratic word problem — often about area or a thrown object’s height — leads to an ax² + bx + c = 0 equation; solve it, then keep only the answer that makes real-world sense.
- Quadratic Formula
- Solving Quadratics by Factoring Factoring solves a quadratic by writing it as two binomials that multiply to zero, then using the zero product property: if (x + 2)(x + 3) = 0, then x = −2 or x = −3.
Linked concepts (purple →) have a full explanation. Hover or tap a dotted ⓘ concept for a quick definition.
Inside the app, Quadratic Equations comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
24/7 AI Tutor — Ask anything and get a step-by-step explanation when you’re stuck — it teaches the concept, not just the answer. Every answer verified by three independent AIs.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
Practice Quadratic Equations with your AI Tutor
Interactive lessons, quizzes, and a 24/7 AI Tutor — every answer verified by three independent AI systems. Currently free for individual users.
Create your free account →