Students continue their study of quadratic equations, learning new strategies to determine the vertex and roots of quadratic equations and applying these in various real-world contexts.
Math
Unit 8
9th Grade
In Unit 8, Quadratic Equations and Applications, students continue their study of quadratic equations from Unit 7. They learn the three common forms of a quadratic equation—standard form, intercept form, and vertex form—and understand how to use these forms efficiently based on the situation at hand. Students also learn new strategies to determine the vertex and the roots of a quadratic equation and then apply these strategies in various real-world contexts.
In Topic A, students are introduced to the vertex form of a quadratic equation. They use their factoring skills from Unit 7 to determine the process of completing the square. Using the process of completing the square, students are able to derive the famous quadratic formula, enabling them to solve for the roots of any quadratic equation. Students investigate examples of quadratic equations with two, one, and no real roots, and make the connection of the number of real roots to the value of the discriminant. Throughout the lessons in this topic, students pay attention to the structure of the equations to determine which strategy and approach are the most efficient way to solve.
In Topic B, students recall how replacing the function $${{f(x)}}$$ with functions such as $${f(x+k)}$$ or $${{f(x)}}+k$$ transforms the graph of $${{f(x)}}$$ in predictable ways. Students then write and analyze quadratic functions to represent different real-world applications involving projectile motion, profit and revenue models, and geometric area applications. Lastly, students investigate systems of equations where one of the equations is a quadratic equation.
Pacing: 17 instructional days (15 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 8 and should be given on the suggested assessment day or after completing the unit.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Vertex form | Quadratic formula |
Intercept form | Discriminant |
Standard form | Projectile motion |
Complete the square | Revenue |
Topic A: Deriving the Quadratic Formula
Topic B: Transformations and Applications
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 7
Quadratic Functions and Solutions