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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.](./probs2_files/image002.gif)
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.](./probs2_files/image024.gif)
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Quadratic Equation Problems homework questions |