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Quadratic Functions

Quadratic Equations

Problems/Quadratic Functions

Problems/Quadratic Equations

Radicals

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:

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.

 

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

 

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:

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.

 

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

 

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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