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: