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Quadratic Functions

Quadratic Equations

Problems/Quadratic Functions

Problems/Quadratic Equations

Radicals - Irrational Expressions

Complex Numbers 1

Complex Numbers 2

Reciprocal Functions

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UNIT 3  : QUADRATIC FUNCTIONS & EQUATIONS

 LESSON 4:  PROBLEM SOLVING WITH QUADRATIC EQUATIONS

 

 

 Quadratic Equation Problems

 

Text Box: Strategies for Solving Quadratic Equations Problems.
·	Determine what is unknown or what you are asked to find. Draw a diagram if possible.
·	Assign variables to these unknowns.  You can use a single variable as in examples 3 & 4 or use two variables as in examples 1 & 2.  These are your let statements.
·	Translate the information in the problem into an algebraic equation.
·	Write this as an equation in one variable if needed  [ see examples 1 & 2 ].
·	Put all the terms on one side of the equation and solve by factoring or the quadratic formula.
 

 

 

 

 

 

 

 

 

 

 


Number Problems:

Example 1:

Two integers differ by 4.  The sum of their squares is 250.  Find the integers.

Solution:

à Determine what is unknown or what you are asked to find?  Assign variables to the unknowns.

 Here we are asked to find two numbers.   Let the first number be x and the second number be y.

 

à  We are told the sum of their squares is 250.  Write this statement as an equation.

                          

 

à  Write this as an equation in one variable.

Since the integers differ by 4, we have a secondary relation between the two variables, namely,

                       

 

 

Check (i)  The integers differ by 4.

            (-9)-(-13) = 4  and  13 – 9 = 4

Check(ii)  The sum of their squares is 250.

            (-9)2 + (-13)2 = 81 + 169 = 250  and

              92 + 132 = 81 + 169 = 250

 

Example 2:

The sum of two numbers is 25 and their product is 156.  Find the numbers.

Solution:

à Determine what is unknown or what you are asked to find?  Assign variables to the unknowns. 

Here we are asked to find two numbers.    Let the first number be x and the second number be y.

 

à  We are told their product is 156.  Write this statement as an equation.

                          

 

à  Write this as an equation in one variable. 

Since their sum is 25, we have a secondary relation between the two variables, namely,

 

 

Check (i)  Their sum is 25

            12 + 13 = 25

Check (ii)  Their product is 156

            (12)(13) = 156

 

 

Area Problems:

 

 

 

 

                      x + 7

 

x

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                                                                                                           x

 
           

 

 

 

 

 


(60+2x)

 

 

 

                                          (80 + 2x)

 

 


 

 


 

 

                                   x

 

 
 

 


           y

 

 

 

                                   

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Text Box: Strategies for Solving Quadratic Equations Problems.
·	Determine what is unknown or what you are asked to find. Draw a diagram if possible.
·	Assign variables to these unknowns.  You can use a single variable as in examples 3 & 4 or use two variables as in examples 1 & 2.  These are your let statements.
·	Translate the information in the problem into an algebraic equation.
·	Write this as an equation in one variable if needed  [ see examples 1 & 2 ].
·	Put all the terms on one side of the equation and solve by factoring or the quadratic formula.
 

 

 

 

 

 

 

 

 

 

 

 


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