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SAT/Sphere
The all-in-one SAT prep platform for everyone!
© 2025 SAT/Sphere. All rights reserved.
SAT/Sphere
The all-in-one SAT prep platform for everyone!
© 2025 SAT/Sphere. All rights reserved.
Find the perfect SAT prep plan designed to match your goals, study style, and budget. Begin your journey to top scores and college admission success with SAT Sphere!
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This SAT Sphere lesson focuses on essential SAT test topics in the Quadratic Equations section. You'll build a strong understanding of core concepts, learn time-saving test-taking strategies, and apply your knowledge to realistic Digital SAT practice questions.
01
Introduction to Quadratic Equations
Frames why quadratics matter on the Digital SAT and reminds students to recall multiplying expressions, combining like terms, solving linear equations, and simplifying radicals.
02
Quadratic Forms and Key Vocabulary
Defines standard, factored, and vertex forms—plus terms like coefficient, root, vertex, and axis of symmetry—refreshing earlier work with polynomial structure and exponent rules.
03
The Discriminant and Nature of Roots
Introduces Δ = b² − 4ac to classify two, one, or zero real roots, building on Radical Expressions and Complex Numbers to interpret square‑root and negative‑root cases.
04
Solving by Factoring
Teaches the zero-product property for quadratics that factor neatly, extending the FOIL and common-factor skills mastered in Multiplication of Expressions.
05
Practice: Factoring Method
Provides timed SAT-style questions so students automate the factoring process introduced in the previous slide.
06
Solving by Completing the Square
Shows how to create a perfect-square trinomial and isolate x, refreshing equation-balancing steps and perfect-square binomial patterns from earlier algebra lessons.
07
Practice: Completing the Square
Offers scaffolded problems that reinforce each algebraic move in the completing‑the‑square method just taught.
08
Deriving and Using the Quadratic Formula
Derives x = [−b ± √(b²−4ac)]⁄2a from completing the square and applies it to any quadratic, extending radical manipulation skills.
09
Practice: Quadratic Formula
Gives SAT-style items where students plug a, b, c into the formula and interpret results in light of the discriminant introduced earlier.
10
Graphing Parabolas and Key Features
Guides students to sketch a parabola using vertex, axis, and intercepts, building on prior coordinate-plane plotting from Systems of Equations.
11
Choosing the Fastest Method
Compares factoring, completing the square, and the quadratic formula so students can select the quickest strategy under SAT timing constraints, synthesizing all solution techniques.
12
Key Takeaways and Mixed Practice
Synthesizes all quadratic solution methods into a mini-quiz and summary sheet, highlighting common pitfalls and time-saving checks.
View Example SAT Lesson with Practice Questions and Explanations
Each SAT Sphere lesson is a focused, interactive learning experience aligned with the new Digital SAT exam format. Lessons include SAT practice questions, detailed explanations, and concept reviews to support your SAT Math or Reading and Writing preparation. Designed for measurable improvement, our SAT lessons build confidence and mastery one topic at a time.
Engage with interactive SAT content featuring real-time practice and instant feedback.
Get personalized SAT prep tips and study guidance tailored to your strengths and weaknesses.
Access a complete Digital SAT curriculum that covers all tested topics and question types.
Build Your Digital SAT Skills with the Advanced Algebra and Functions Module
This lesson is part of the Advanced Algebra and Functions module, a structured SAT prep unit designed to improve your performance in key areas of the Digital SAT. Each module includes multiple SAT-focused lessons that develop critical thinking, analytical skills, and test-taking confidence. Progress through each module to strengthen your understanding and raise your overall SAT score.
Advance your SAT preparation by completing other SAT Sphere lessons in the Advanced Algebra and Functions module. Each lesson targets a specific concept tested on the Digital SAT, helping you deepen your knowledge and refine your skills for the real exam.
08
Modules
SAT Sphere includes 8 focused modules that cover every topic tested in the Math and Reading & Writing sections of the Digital SAT. Each module is built to strengthen core skills and test-taking ability.
86
Lessons
With 86 in-depth lessons, SAT Sphere helps you understand key SAT concepts clearly and efficiently. Our lessons break down each topic into simple, actionable parts.
10k+
Practice
Apply your knowledge using interactive SAT-style practice questions. Get immediate insights with feedback and explanations that help you improve fast.
+6k
Flash cards
Reinforce your learning with more than 6900 flash cards. Use them to review vocabulary, grammar, math facts, and more — anytime, anywhere.
Personalized study plan
Stay organized with our AI-powered study planner. Set your test date and daily study goals, and get a custom SAT prep plan tailored to your pace. Make consistent progress and be fully prepared by test day.
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SAT/AI gives you personalized, step-by-step guidance that fits your learning style. Stuck on a tough math problem or confused by a reading passage? SAT/AI breaks it down clearly, offers instant feedback, and helps you learn from mistakes—building your confidence and boosting your score, one question at a time.
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Begin your SAT preparation with SAT Sphere's comprehensive Digital SAT course. Access expertly crafted SAT lessons, interactive practice questions, and proven strategies to improve your SAT Math and SAT Reading and Writing scores. Whether you're aiming for a perfect 1600 or looking to boost your score, SAT Sphere guides you step-by-step toward SAT success.
Explore quadratic equations by factoring, completing the square, and using the quadratic formula. Work through SAT-style drills to deepen your parabola understanding. Master every quadratic challenge on test day.
Master the SAT with our targeted lesson on Quadratic Equations, part of SAT Sphere’s Digital SAT curriculum. This lesson delivers in-depth concept explanations, problem-solving techniques, and SAT-style practice questions to help you improve your SAT performance. Ideal for both SAT Math and Reading & Writing, each lesson helps you build confidence for test day.