evaluate algebraic expressions

Contents:   Intro & Vocabulary   Examples   Exercises   Evaluate a Function   Repeating the Process Prior to Point-Plotting  


Intro & Vocabulary


      Usually, the instruction evaluate, simplify given all information, is introduced in algebra, and not used in arithmetic.

      One replaces the values of the variables with a constant or expression, then, simplifies the expression until a constant remains or like terms have been combined. [See Combine Like Terms.]

      When parentheses, (   ), are used, the task is simplified. The parentheses indicate the value of the variable is to be used. [Please read Writing One Operation Equations, Expressions, & Statements or just the use of "of" and check out the example given below which illustrates the meaning and use of parentheses.

 
Examples
 
1. Evaluate x2 - 3xy + 2y when x= -1 and y = 2
 
1a.)
    the meaning of parentheses          
    x2 - 3xy + 2y
    (x)2 - 3(x)(y) + 2(y)
  (-1)2 - 3(-1)(2) + 2(2)
  +1 + 6 + 4
    11, the answer    
1b.)
the way it usually looks          
    x2 - 3xy + 2y
    (-1)2 - 3(-1)(2) + 2(2)
    +1 + 6 + 4
    11, the answer
       
1c.)
    middle ground, writing each step out
    x2 - 3xy + 2y
  (  )2 - 3(  )(  ) + 2(  )
(-1)2 - 3(-1)(2) + 2(2)
  +1 + 6 + 4
    11, the answer
 
2. State f(2), f(-1), f(4) when f(x) = 2x + 4
2a.) x is 2
    f(x) = 2x + 4      
    f(2) = 2(2) + 4
    f(2) = 4 + 4
    f(2) = 8                                
2b.) x is -1
    f(x) = 2x + 4      
    f(-1) = 2(-1) + 4
    f(-1) = -2 + 4
    f(-1) = 2                        
2c.) x is 4
    f(x) = 2x + 4      
    f(4) = 2(4) + 4
    f(4) = 8 + 4
    f(4) = 12
 
Exercises
Evaluate the expression when x = - 3 and y = 2.
3.)     x² - y
 
4.)     4x - y
 
5.)     4x - 3y
 
6.)     xy - (x + y)
 
 
7.) Evaluate 2x² + xy   when x is -1 and y = 4
 
Evaluate a Function  
8. Evaluate when f(x) = (x+1)² then MOUSEOVER the arrow to see the answer.
a.) f(3) 16
b.) f(-1) 0
c.) f(a) (a+1)²
d.) f(x - h) (x - h + 1)²
 
 
Repeating the Process Prior to Point-Plotting

      In the above exercises, the same expression was used with different values of the variable. This procedure is required when generating points for point-plotting the graph of a function.

9. Complete the table of values and graph the line y = 4x + 2      
xy
0   
-1/2 
2 
-5/4 
9. Complete the table of values and graph the line y = 4x + 2      
evaluation showing work
xy=4x+2
04(0)+2=0+2= 2
-1/24(-1/2)+2= -2 + 2= 0
24(2)+2=8+2= 10
-5/44(-5/4)+2= -5 + 2= -3
ordered pairs
xy
02
-1/20
210
-5/4-3
Complete the table. MOUSEOVER the arrow to see the answer .
10.) (0,2),(8,0),(-4,3),(-32,10)
x y = -x/4 + 2
0 
8 
-4 
-32 
                11.) (-1,8),(3,0),(2,2),(0,6)
xy= 6 - 2x
-1  
3  
2  
0  



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