6.6 Applications of Quadratic Equations
Solving an Applied Problem
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Read the problem carefully until you understand what is given and what is to be found.
Assign a variable to represent the unknown value, using diagrams or tables as needed.
Write down what the variable represents. If necessary, express any other unknown
values in terms of the variable.
Write an equation using the variable expression(s).
Solve the equation.
State the answer. Does it seem reasonable?
Check the answer in the words of the original problem.
Example 1: Area of a parallelogram:
The area of this parallelogram is
sq. units. Find its base and height.
Example 2: Area of a rectangle:
A hardcover book is 3
longer than it is wide. The area of the cover is 54
length and width of the book.
Example 3: Volume of a rectangular box:
The volume of this rectangular box is 192 cu. units. Find its length and width.
4
x
x+2
Find the
Example 4: Area of a triangle:
The area of a triangle is 24
. The base of the triangle measures
height. Find the measures of the base and the height.
more than the
Two consecutive integers:
Two consecutive even or odd integers:
Example 5:
The product of the first and third of three consecutive odd integers is 16 more than the
middle integer. Find the integers.