Lesson 9 | Quadratic Equations and Applications | 9th Grade Mathematics

Objective

Describe transformations to quadratic functions. Write equations for transformed quadratic functions.

Lesson Map

Topic A: Deriving the Quadratic Formula

Lesson

Describe features of the vertex form of a quadratic function and write quadratic equations in vertex form from graphs.

Standards

A.SSE.B.3F.IF.B.4F.IF.C.8

Lesson

Complete the square.

Standards

A.SSE.B.3.B

Lesson

Complete the square to identify the vertex and solve for the roots of a quadratic function.

Standards

A.REI.B.4.BA.SSE.B.3.B

Lesson

Solve and interpret quadratic applications using the vertex form of the equation.

Standards

A.SSE.B.3.BF.IF.C.8.A

Lesson

Convert and compare quadratic functions in standard form, vertex form, and intercept form.

Standards

F.IF.B.4F.IF.C.9

Lesson

Derive the quadratic formula. Use the quadratic formula to find the roots of a quadratic function.

Standards

A.REI.B.4.A

Lesson

Determine the number of real roots of a quadratic function using the discriminant of the quadratic formula.

Standards

A.REI.B.4.BF.IF.C.7.A

Lesson

Graph quadratic functions from all three forms of a quadratic equation.

Standards

F.IF.C.7.A

Topic B: Transformations and Applications

Lesson

Describe transformations to quadratic functions. Write equations for transformed quadratic functions.

Standards

F.BF.B.3

Lesson

Graph and describe transformations to quadratic functions in mathematical and real-world situations.

Standards

F.BF.B.3

Lesson

Write and analyze quadratic functions for projectile motion and falling bodies applications.

Standards

A.CED.A.2F.IF.C.8.AF.IF.C.9

Lesson

Write and analyze quadratic functions for geometric area applications.

Standards

A.CED.A.2F.IF.C.8.A

Lesson

Write and analyze quadratic functions for revenue applications.

Standards

A.CED.A.2F.BF.A.1.BF.IF.C.8.A

Lesson

Solve and identify solutions to systems of quadratic and linear equations when two solutions are present.

Standards

A.REI.C.7A.REI.D.11

Lesson

Solve and identify solutions to systems of quadratic and linear equations when two, one, or no solutions are present.

Standards

A.REI.C.7A.REI.D.11

Quadratic Equations and Applications

Objective

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Quadratic Equations and Applications

Objective

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