May 21st
May 21st
Evaluation of Simple Formulas
To evaluate an algebraic expression means to
substitute given numbers for each literal symbol in the
expression and then carry out the indicated arithmetic to obtain
a single numerical value for the entire expression.
Example:
Evaluate 3x 2 – 5x + 7 for x = 2 and for x =
-5.
solution:
When x = 2, the expression becomes
3x 2 – 5x + 7 = 3(2) 2 – 5(2)
+ 7
= 3(4) – 5(2) + 7
= 12 – 10 + 7
= 9
When x = -5, we get
3x 2 – 5x + 7 = 3(-5) 2 –
5(-5) + 7
= 3(25) – 5(-5) + 7
= 75 + 25 + 7
= 107
Notice the use of brackets where convenient, particularly to
ensure the correct handling of negative numbers.
Example:
Evaluate  when x = -3.
solution:
Substituting
We needed to take considerable care here to handle the
negative numbers correctly.
Example:
Evaluate  when a = 2 and when a
= -2.
solution:
When a = 2, we get
When a = -2, we get
So, we get the same value for both a = +2 and for a = -2.
Although (3) 2 = 9 and (-3) 2 = 9, so that
both +3 and -3 are square roots of 9, the symbol  stands for the positive
square root of 9 by definition. Thus, is always considered to
be +3.
Example:
Evaluate x 2 – 5x + 4 for x = 0, 1, 2, 3, 4,
and 5.
solution:
Here it is probably easiest to just make a table summarizing
our results:
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