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:
