1.4 Quadratic Equations

Miller & Gerken, College Algebra 2e — Pages 128-143

Learning Objectives

  • Solve quadratic equations by factoring

  • Solve using the square root property

  • Complete the square

  • Apply the quadratic formula

  • Use the discriminant to determine solution types

Key Concepts

Standard Form

\[ax^2 + bx + c = 0, \quad a \neq 0\]

Quadratic Formula

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Discriminant

\[\Delta = b^2 - 4ac\]
Discriminant Nature of Roots

\(\Delta > 0\)

Two distinct real solutions

\(\Delta = 0\)

One repeated real solution

\(\Delta < 0\)

Two complex conjugate solutions

Completing the Square

For \(x^2 + bx\):

\[x^2 + bx + \left(\frac{b}{2}\right)^2 = \left(x + \frac{b}{2}\right)^2\]

Examples

Example 1. Example 1 (p. XX)

Work through textbook example…​

Practice Problems

Problem 1 (p. XX, #YY)

Problem:

My Work:

Answer:

Section Summary

  1. Key point 1

  2. Key point 2

  3. Key point 3

Study Notes

Personal observations and things to remember…​

Next: 1.5 Quadratic Applications