Learn on PengienVision, Algebra 2Chapter 2: Quadratic Functions and Equations

Lesson 3: Factored Form of a Quadratic Function

In this Grade 11 enVision Algebra 2 lesson, students learn how to factor quadratic expressions, apply the Zero Product Property, and find the zeros of quadratic functions using factored form. The lesson covers factoring techniques including factor pairs, factoring by grouping, and solving equations like 2x² + 9x = 5 by setting each factor equal to zero. Students also explore real-world applications, such as using a quadratic function to determine when a projectile hits the ground.

Section 1

Factoring Quadratic Expressions (Leading Coefficient 1)

Property

To factor a quadratic expression of the form $x^2 + bx + c$ , find two numbers that multiply to $c$ and add to $b$ . The factored form is $(x + m)(x + n)$ where $m \cdot n = c$ and $m + n = b$ .

Examples

Section 2

The zero-factor principle

Property

If the product of two numbers is zero, then one (or both) of the numbers must be zero. Using symbols,

If $AB = 0$ , then either $A = 0$ or $B = 0$ .

Examples

To solve $(x - 7)(x + 3) = 0$ , set each factor to zero. $x - 7 = 0$ gives $x = 7$ , and $x + 3 = 0$ gives $x = -3$ .

Section 3

Solving quadratic equations by factoring

Property

To Solve a Quadratic Equation by Factoring:

Write the equation with zero isolated on the right side.

Factor the left side of the equation.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Factoring Quadratic Expressions (Leading Coefficient 1)

Property

To factor a quadratic expression of the form $x^2 + bx + c$ , find two numbers that multiply to $c$ and add to $b$ . The factored form is $(x + m)(x + n)$ where $m \cdot n = c$ and $m + n = b$ .

Examples

Section 2

The zero-factor principle

Property

If the product of two numbers is zero, then one (or both) of the numbers must be zero. Using symbols,

If $AB = 0$ , then either $A = 0$ or $B = 0$ .

Examples

To solve $(x - 7)(x + 3) = 0$ , set each factor to zero. $x - 7 = 0$ gives $x = 7$ , and $x + 3 = 0$ gives $x = -3$ .

Section 3

Solving quadratic equations by factoring

Property

To Solve a Quadratic Equation by Factoring:

Write the equation with zero isolated on the right side.

Factor the left side of the equation.

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Factoring Quadratic Expressions (Leading Coefficient 1)

Property

To factor a quadratic expression of the form $x^2 + bx + c$ , find two numbers that multiply to $c$ and add to $b$ . The factored form is $(x + m)(x + n)$ where $m \cdot n = c$ and $m + n = b$ .

Examples

Section 2

The zero-factor principle

Property

If the product of two numbers is zero, then one (or both) of the numbers must be zero. Using symbols,

If $AB = 0$ , then either $A = 0$ or $B = 0$ .

Examples

To solve $(x - 7)(x + 3) = 0$ , set each factor to zero. $x - 7 = 0$ gives $x = 7$ , and $x + 3 = 0$ gives $x = -3$ .

Section 3

Solving quadratic equations by factoring

Property

To Solve a Quadratic Equation by Factoring:

Write the equation with zero isolated on the right side.

Factor the left side of the equation.