The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 5.22: SOLVING QUADRATIC EQUATIONS USING

THE QUADRATIC FORMULA

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The quadratic formula states thatx=

−b±

√

b^2 − 4 ac

2 a

wherea=0andb^2 − 4 ac≥ 0 .Youcan

use the quadratic formula to solve a quadratic equation that is written in standard form,

ax^2 +bx+c= 0 , wherea=0. Follow the steps below:

1. Write the equation in standard form. Identify the numbers that correspond to the vari-
   ablesa,b,andc. Substitute these values in the quadratic formula.


2. Write the quadratic formula as two equations: one that adds the square root and one
   that subtracts the square root.


3. Simplify using the order of operations to find the solutions.


4. Substitute these solutions in the original equation to check your work.

EXAMPLE

x^2 + 3 x+ 2 = 0 Use the quadratic formula to solve forx. a= 1 ,b= 3 ,c= 2

x=

− 3 ±

√

32 −4(1)(2)

2(1)

→x=

− 3 +

√

32 −4(1)(2)

2(1)

orx=

− 3 −

√

32 −4(1)(2)

2(1)

x=

− 3 +

√

9 − 8

2

orx=

− 3 −

√

9 − 8

2

x=− 1 andx=− 2 Check:(−1)^2 +3(−1)+ 2 = 0 and(−2)^2 +3(−2)+ 2 = 0

DIRECTIONS: Use the quadratic formula to solve each equation.

1. x^2 − 5 x+ 6 = 0 2. x^2 − 3 x− 4 = 0


2. x^2 + 9 x+ 18 = 0 4. x^2 + 10 x=− 25

CHALLENGE:Explain how you would solvex^2 =−x+12 by using the

quadratic formula.

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©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.