Expressions and One-Variable Equations
Variables, equivalence, and balance
Math workbook
Quadratics: Patterns, Graphs, and Solutions: Tables, forms, methods, and models
Grades 9–12Level 4
About this book
See the pattern, choose the form, and check the answer.
This workbook helps learners in grades 9–12 make sense of quadratics. It starts with tables and second differences, then shows how standard, factored and vertex forms each reveal a different feature of a parabola. Learners solve equations by factoring, square roots, completing the square or the quadratic formula, and check every solution. The last module uses simple stated models of area and motion and asks which answers make sense. Each module moves from a plain explanation to worked examples, guided and independent practice, and spaced review. An explanatory answer key at the back supports adults who check the work.
- Spot quadratic patterns with equal-step difference tables
- Read zeros, vertex and intercept from the best form
- Solve by factoring, square roots or the quadratic formula
- Reject roots that a context does not allow
- Answer key with reasons and common-error notes
For learners in grades 9–12 who can solve linear equations and multiply two binomials.
Look inside
What this book covers
Covered
- This book is about quadratics: expressions and functions of degree two, such as x² − 6x + 8.
- You will spot quadratic patterns in tables, read features of a parabola from three forms, solve quadratic equations with real solutions, and decide which answers make sense in a context.
- Pages 53–55 add completing the square and function notation f(x).
Not covered
Not in this book: complex-number solutions, quadratic inequalities, systems of equations and higher-degree polynomials.
Before you start
If lines and slope feel shaky, work through Linear Equations and Graphs first.
Things to have
- You need a pencil, an eraser and a scientific calculator for square roots.
- Graph paper helps but is not required.
Notice
Pictures in this book are simplified learning models. Check answers with the explanations at the back of the book.
The steps in this book
- Step 1: Readiness Check
Check the skills you need before you begin. If something feels tricky, an adult can help you start in the right place.
- Step 2: Concept
Read a short, clear explanation of the new idea and the words that go with it.
- Step 3: Worked Example
Watch the idea being used, one step at a time, in a worked example.
- Step 4: Guided Practice
Practice with prompts and help cues. The help gets smaller as you get stronger.
- Step 5: Independent Practice
Practice on your own with different kinds of questions, and explain your thinking.
- Step 6: Review
Look back at earlier learning so it stays strong, then check where to go next.
- Step 7: Answers and Explanations
Check your answers. Each answer explains why, names a common mistake, and shows how to fix it.
What is in the book
The modules
- Module 1: Recognize quadratic structurePages 5–14
- Module 2: Forms reveal different graph featuresPages 15–24
- Module 3: Solve with a justified methodPages 25–34
- Module 4: Interpret quadratic modelsPages 35–44
Contents
- Readiness check, pp. 3–4. Before Module 1. Its table tells you where to start.
- Modules, pp. 5–44
- Checkpoints, pp. 14, 24, 34, 44. The last page of each module.
- Mixed review, pp. 45–48. Questions from across the book, mixed together.
- Exit check, pp. 49–50. A last check across the book.
- Reflect and repair, p. 51
- Try again, p. 52. Fresh questions like those in the exit check.
- Further practice, pp. 53–55. More pages of step 5, Independent Practice.
- Extra practice, pp. 56–58
- Answers and explanations, pp. 59–68. Notes in this part are headed “Why”, “Common mistake” and “Help”.
Other books it mentions
Before this book
Linear Equations and Graphs
Tables, slopes, equations and systems
Integer Operations: From Number Lines to Rules
Number lines, counters, and patterns
After this book
College Algebra: Functions and Graphs
Domains, composition, inverses, and models