Print this Page

3.4 – Solving Quadratic Equations

Objectives

  • Write quadratic equations in the standard form.
  • Apply the zero product rule to find the solutions to an equation.
  • Solve quadratic equations that contain perfect square trinomials.
  • Choose the correct steps to solve quadratic equations in various forms.

 

Key Terms

  • Quadratic Equation – An equation that has, or could be simplified to have, the standard form: ax^2+bx+c=0
  • Zero Product Rule – A rule stating that if A and B are two quantities: AB = 0, then A = 0, B = 0 or both.
    • Example: x^2-5x+4=0
    • Factor: (x-4)(x-1)=0
    • Apply the Zero Product Rule: x-4=0 and x-1=0
    • Solve for x: x=4 and x=1

Notes

Solving Quadratic Equations
  • Factor the quadratic expression in the equation.
  • Use the zero product rule to set up smaller equations.
  • Solve the resulting equations
  • Review

Alg2A 3.04 - Review01

  • Set each expression equal to zero

Alg2A 3.04 - Zero Product Rule 01

Examples
  • Example 1: Zero Product Rule
    • Step 1: Factor
    • Step 2: Set each factor equal to zero
    • Step 3: Solve for x

Alg2A 3.04 - Change to Stnd Form Ex

  • Example 2: Zero Product Rule
    • Step 1: Factor
    • Step 2: Set each factor equal to zero
    • Step 3: Solve for x

Alg2A 3.04 - Zero Product Rule 02

 Then check your work using substitution!

Alg2A 3.04 - Zero Product Rule 02

  • Sometimes, you will convert equations to Standard Form before factoring

Alg2A 3.04 - Change to Stnd Form Rule

Alg2A 3.04 - Change to Stnd Form

  • Sometimes, you will NOT convert equations to Standard Form before factoring
    • Instead, you will factor, then take the square root of both sides

Alg2A 3.04 - Square Root Both Sides Alg2A 3.04 - No Change to Stnd Form Ex

Permanent link to this article: http://newvillagegirlsacademy.org/math/?page_id=1707