# 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

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

• Set each expression equal to zero

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

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

Then check your work using substitution!

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

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