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.
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.
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Vertex form | Quadratic formula |
Intercept form | Discriminant |
Standard form | Projectile motion |
Complete the square | Revenue |
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
This assessment accompanies Unit 8 and should be given on the suggested assessment day or after completing the unit.
F.IF.B.4
A.SSE.B.3
F.IF.C.8
Describe features of the vertex form of a quadratic function and write quadratic equations in vertex form from graphs.
A.SSE.B.3.B
Complete the square.
A.SSE.B.3.B
A.REI.B.4.B
Complete the square to identify the vertex and solve for the roots of a quadratic function.
A.SSE.B.3.B
F.IF.C.8.A
Solve and interpret quadratic applications using the vertex form of the equation.
F.IF.B.4
F.IF.C.9
Convert and compare quadratic functions in standard form, vertex form, and intercept form.
A.REI.B.4.A
Derive the quadratic formula. Use the quadratic formula to find the roots of a quadratic function.
F.IF.C.7.A
A.REI.B.4.B
Determine the number of real roots of a quadratic function using the discriminant of the quadratic formula.
F.IF.C.7.A
Graph quadratic functions from all three forms of a quadratic equation.
F.BF.B.3
Describe transformations to quadratic functions. Write equations for transformed quadratic functions.
F.BF.B.3
Graph and describe transformations to quadratic functions in mathematical and real-world situations.
F.IF.C.8.A
F.IF.C.9
A.CED.A.2
Write and analyze quadratic functions for projectile motion and falling bodies applications.
F.IF.C.8.A
A.CED.A.2
Write and analyze quadratic functions for geometric area applications.
F.IF.C.8.A
F.BF.A.1.B
A.CED.A.2
Write and analyze quadratic functions for revenue applications.
A.REI.C.7
A.REI.D.11
Solve and identify solutions to systems of quadratic and linear equations when two solutions are present.
A.REI.C.7
A.REI.D.11
Solve and identify solutions to systems of quadratic and linear equations when two, one, or no solutions are present.
Key: Major Cluster Supporting Cluster Additional Cluster
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