 ### 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) b.) f(-1) c.) f(a) d.) f(x - h) 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
 x y 0 -1/2 2 -5/4
9. Complete the table of values and graph the line y = 4x + 2
evaluation showing work
 x y=4x+2 0 4(0)+2=0+2= 2 -1/2 4(-1/2)+2= -2 + 2= 0 2 4(2)+2=8+2= 10 -5/4 4(-5/4)+2= -5 + 2= -3
ordered pairs
 x y 0 2 -1/2 0 2 10 -5/4 -3 Complete the table. MOUSEOVER the arrow to see the answer .
10.) x y = -x/4 + 2 0 8 -4 -32
11.) x y= 6 - 2x -1 3 2 0

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