D.1. Graph Quadratic Functions in Standard Form

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2. D.1.Q. Unit Challenge

3. D.1.1. Quadratic Parent Function y = x²

   1. D.1.1.1. Graphing y = ax² by Making a Table of Values
   2. D.1.1.2. Graphing y = ax² + c by Making a Table of Values

4. D.1.2. Standard Form y = ax² + bx + c

   1. D.1.2.1. Identifying the Vertex as Max or Min Given the Graph
   2. D.1.2.2. Identifying the Vertex as Max or Min Given Standard Form
   3. D.1.2.3. Finding the Vertex Given Standard Form
   4. D.1.2.4. Finding the Axis of Symmetry
   5. D.1.2.5. Graphing y = ax² + bx + c Using the Table of Values
   6. D.1.2.6. Graphing y = ax² + bx + c Using the Vertex

5. D.1.3. Word Problems Involving Graphing Quadratic Functions

   1. D.1.3.1. Graphing Quadratic Functions Given a Word Problem

D.9. Graph Quadratic Functions in Vertex or Intercept Form

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2. D.9.Q. Unit Challenge

3. D.9.1. Vertex Form y = a(x – h)² + k

   1. D.9.1.1. Identifying the Vertex as Max or Min Given Vertex Form
   2. D.9.1.2. Finding the Vertex Given Vertex Form
   3. D.9.1.3. Graphing y = a(x – h)² + k Using the Vertex
   4. D.9.1.4. Solving Word Problems Using Vertex Form

4. D.9.2. Intercept Form y = a(x + p)(x + q)

   1. D.9.2.1. Identifying the Vertex as Max or Min Given Intercept Form
   2. D.9.2.2. Finding the Vertex Given Intercept Form
   3. D.9.2.3. Graphing y = a(x + p)(x + q) Using the Vertex and X-Intercepts
   4. D.9.2.4. Solving Word Problems Using Intercept Form

5. D.9.3. Changing Between Vertex, Intercept and Standard Form

   1. D.9.3.1. Changing from Intercept to Standard Form
   2. D.9.3.2. Changing from Vertex to Standard Form

D.8. Factoring x² + bx + c Trinomials

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2. D.8.Q. Unit Challenge

3. D.8.1. Basic x² + bx + c Trinomials

   1. D.8.1.1. Factoring x² + bx + cTrinomials
   2. D.8.1.2. Determining if x² + bx + c Trinomials Can be Factored

4. D.8.2. Factoring Special Products

   1. D.8.2.1. Factoring the Difference of Two Squares
   2. D.8.2.2. Factoring Perfect Square Trinomials

5. D.8.3. Solving x² + bx + c = 0

   1. D.8.3.1. Solving x² + bx + c = 0 Using the Zero Product Property
   2. D.8.3.2. Solving Word Problems Using the Zero Product Property

6. D.8.4. Finding Zeroes of Quadratic Functions

   1. D.8.4.1. Finding Zeroes of Quadratic Functions by Factoring

7. D.8.5. Solving Problems Involving Factoring x² + bx + c Trinomials

   1. D.8.5.1. Solving x² + bx + c = 0 Given Geometric Area Problems

D.7. Factoring ax² + bx + c Trinomials

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2. D.7.Q. Unit Challenge

3. D.7.1. Basic ax² + bx + c Trinomials

   1. D.7.1.1. Factoring ax² + bx + c Trinomials (c >0)
   2. D.7.1.2. Factoring ax² + bx + c Trinomials (c <0)
   3. D.7.1.3. Determining if ax² + bx + c Trinomials Can be Factored

4. D.7.2. Factoring Special Products

   1. D.7.2.1. Factoring the Difference of Two Squares
   2. D.7.2.2. Factoring Perfect Square Trinomials

5. D.7.3. Removing Common Factors

   1. D.7.3.1. Factoring Trinomials by Removing Common Factors First

6. D.7.4. Solving ax² + bx + c = 0

   1. D.7.4.1. Solving ax² + bx + c = 0 Using the Zero Product Property
   2. D.7.4.2. Solving Word Problems Using the Zero Product Property

7. D.7.5. Finding Zeroes of Quadratic Functions

   1. D.7.5.1. Finding Zeroes of Quadratic Functions by Factoring

8. D.7.6. Solving Problems Involving ax² + bx + c Trinomials

   1. D.7.6.1. Solving ax²Â + bx + c = 0 Given Geometric Area Problems

D.6. Solve Quadratic Equations by Finding Square Roots

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2. D.6.Q. Unit Challenge

3. D.6.1. Properties of Square Roots

   1. D.6.1.1. Simplifying Expressions Using the Product Property
   2. D.6.1.2. Simplifying Expressions Using the Quotient Property

4. D.6.2. Rationalizing the Denominator

   1. D.6.2.1. Rationalizing the Denominator of the Form √b
   2. D.6.2.2. Rationalizing the Denominator of the Form a + √b
   3. D.6.2.3. Rationalizing the Denominator of the Form a - √b

5. D.6.3. Solving Quadratic Equations

   1. D.6.3.1. Solving Quadratic Equations Using Square Roots

6. D.6.4. Solving Problems by Finding Square Roots

   1. D.6.4.1. Solving Word Problems Using Square Roots

D.5. Perform Operations with Complex Numbers

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2. D.5.Q. Unit Challenge

3. D.5.1. Imaginary Numbers

   1. D.5.1.1. Simplifying Expressions by Using Imaginary Numbers

4. D.5.2. Solving Quadratic Equations

   1. D.5.2.1. Solving Quadratic Equations by Using Imaginary Numbers

5. D.5.3. Operations with Complex Numbers

   1. D.5.3.1. Adding Complex Numbers
   2. D.5.3.2. Subtracting Complex Numbers
   3. D.5.3.3. Multiplying Complex Numbers
   4. D.5.3.4. Dividing Complex Numbers

6. D.5.4. The Complex Plane

   1. D.5.4.1. Plotting Complex Numbers in the Complex Plane

7. D.5.5. Absolute Value of Complex Numbers

   1. D.5.5.1. Finding the Absolute Value of Complex Numbers

D.4. Complete the Square

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2. D.4.Q. Unit Challenge

3. D.4.1. Solving Quadratic Equations by Finding Square Roots

   1. D.4.1.1. Solving Quadratic Equations by Finding Square Roots

4. D.4.2. Making Perfect Square Trinomials

   1. D.4.2.1. Finding the c Value that Makes a Perfect Square Trinomial

5. D.4.3. Solving Quadratic Equations by Completing the Square

   1. D.4.3.1. Solving ax² + bx + c = 0 when a = 1
   2. D.4.3.2. Solving ax² + bx + c = 0 when a ≠ 1

6. D.4.4. Solving Problems by Completing the Square

   1. D.4.4.1. Solving Geometric Area Problems by Completing the Square
   2. D.4.4.2. Solving Word Problems by Completing the Square

D.3. Use the Quadratic Formula and the Discriminant

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2. D.3.Q. Unit Challenge

3. D.3.1. Discriminant

   1. D.3.1.1. Finding the Discriminant and Number of Roots Given a Quadratic Equation

4. D.3.2. Quadratic Formula

   1. D.3.2.1. Solving Quadratic Equations with Two Real Roots
   2. D.3.2.2. Solving Quadratic Equations with One Real Root
   3. D.3.2.3. Solving Quadratic Equations with Imaginary Roots

5. D.3.3. Solving Problems Using the Quadratic Formula

   1. D.3.3.1. Solving Word Problems Involving the Vertical Motion Formula

D.2. Graph and Solve Quadratic Inequalities

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2. D.2.Q. Unit Challenge

3. D.2.1. Graphing Quadratic Inequalities

   1. D.2.1.1. Graphing y < ax² + bx + c Quadratic Inequalities
   2. D.2.1.2. Graphing y > ax² + bx + c Quadratic Inequalities
   3. D.2.1.3. Graphing y < ax² + bx + c Quadratic Inequalities
   4. D.2.1.4. Graphing y ≥ ax² + bx + c Quadratic Inequalities

4. D.2.2. Solving Quadratic Inequalities

   1. D.2.2.1. Solving Quadratic Inequalities by Graphing
   2. D.2.2.2. Solving Quadratic Inequalities Algebraically

5. D.2.3. Graphing Systems of Quadratic Inequalities

   1. D.2.3.1. Graphing Systems of Quadratic Inequalities with Solution Sets
   2. D.2.3.2. Graphing Systems of Quadratic Inequalities with No Solution Sets

6. D.2.4. Solving Problems Involving Quadratic Inequalities

   1. D.2.4.1. Solving Quadratic Inequalities Given a Word Problem

D.10. Write Quadratic Functions

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2. D.10.Q. Unit Challenge

3. D.10.1. Writing Quadratic Functions In Vertex Form

   1. D.10.1.1. Writing Quadratic Functions in Vertex Form Given the Vertex and a Point

4. D.10.2. Writing Quadratic Functions in Intercept Form

   1. D.10.2.1. Writing Quadratic Functions in Intercept Form Given the X-Intercepts and a Point

5. D.10.3. Writing Quadratic Functions in Standard Form

   1. D.10.3.1. Writing Quadratic Functions in Standard Form Given Three Points