# Module 3: Quadratic Equations and Quadratic Functions

**Section 3.1.7 Textbook: Graphs of Quadratic Functions**

Section 3.1.7 Textbook: Graphs of Quadratic Functions

**Learning Objectives**

• Graph quadratic functions.

• Compare graphs of quadratic functions.

• Graph quadratic functions in intercept form.

• Analyze graphs of real-world quadratic functions.

**Section 3.1.7 Videos**

**Textbook Section 3.2: Quadratic Equations by Graphing**

Textbook Section 3.2: Quadratic Equations by Graphs

Supplement #1: Graphs of Quadratics

**Learning Objectives**

• Identify the number of solutions of quadratic equations.

• Solve quadratic equations by graphing.

• Find or approximate zeros of quadratic functions.

• Analyze quadratic functions using a graphing calculators.

• Solve real-world problems by graphing quadratic functions.

**Section 3.3 Textbook: Quadratic Equations by Square Roots**

Section 3.3 Textbook: Quadratic Equations by Square Roots

**Learning objectives**

• Solve quadratic equations involving perfect squares.

• Approximate solutions of quadratic equations.

• Solve real-world problems using quadratic functions and square roots.

**Section 3.3 Videos**

**Section 3.4 Textbook: Solving Quadratic Equations by Completing the Square**

Section 3.4 Textbook: Solving Quadratic Equations by Completing the Square

**Learning objectives**

• Complete the square of a quadratic expression.

• Solve quadratic equations by completing the square.

• Solve quadratic equations in standard form.

• Graph quadratic equations in vertex form.

• Solve real-world problems using functions by completing the square.

**Section 3.4 Videos**

**Video Lessons**

**Video Examples**

- Ex: Creating a Perfect Square Quadratic Trinomial Expression
- Ex: Create an Expression with a Perfect Square Quadratic Trinomial
- Ex 1: Completing the Square - Real Rational Solutions
- Ex 2: Completing the Square - Real Irrational Solutions
- Ex 3: Completing the Square - Complex Solutions
- Ex 4: Completing the Square - Leading Coefficient Not 1
- Ex 1: Write a Quadratic Function in Standard Form to Graph
- Ex 2: Write a Quadratic Function in Standard Form to Graph a not 1

**Section 3.5 Textbook: Solving Quadratic Equations by the Quadratic Formula**

Section 3.5 Textbook: Solving Quadratic Equations by the Quadratic Formula

**Learning objectives**

• Solve quadratic equations using the quadratic formula.

• Identify and choose methods for solving quadratic equations.

• Solve real-world problems using functions by completing the square.

**Section 3.5 Videos**

**Video Lessons**

**Video Examples**

- Ex: Simplify a Radical Expression (Quadratic Formula Practice)
- Proof of The Quadratic Formula
- Ex: Quadratic Formula - Two Real Rational Solutions
- Ex: Quadratic Formula - One Real Rational Repeated Solution
- Ex1: Quadratic Formula - Two Real Irrational Solutions
- Ex2: Quadratic Formula - Two Real Irrational Solutions
- Ex: Quadratic Formula - Complex Solutions

**Section 3.6 Textbook: The Discriminant**

Section 3.6 Textbook: The Discriminant

**Learning Objectives**

• Find the discriminant of a quadratic equation.

• Interpret the discriminant of a quadratic equation.

• Solve real-world problems using quadratic functions and interpreting the discriminant.

**Section 3.6 Videos**

**Section 3.7 - 3.8 Textbook: Linear and Quadratic Models**

Section 3.7 - 3.8 Textbook: Linear and Quadratic Models

Section 3.7

Section 3.8

**Learning Objectives**

• Identify functions using differences and ratios.

• Write equations for functions.

• Perform linear and quadratic regressions with a graphing calculator.

• Solve real-world problems by comparing function models.

**Section 3.7-3.8 Videos**

**Video Lessons**

- Introduction to Regression Analysis
- Linear Regression – Example 1, Example 2
- Quadratic Regression – Example 1, Example 2

**Video Examples**

- Ex: Quadratic Function Application - Blood Pressure
- Ex: Find the Size of Cardboard Needed to Make a Box with a Given Volume
- Ex: Quadratic Function Application - Horizontal Distance and Vertical Height
- Ex: Quadratic Function Application - Time and Vertical Height
- Ex: Quadratic Regression on the TI84 - Stopping Distance

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