24 Chapter 1 Real Numbers and Algebraic Expressions The first skill we need is the ability to evaluate algebraic expressions. To evaluate an algebraic expression means to find the value of an expression for a specific value of the variable. Procedure: Evaluating an Algebraic Expression Step 1: Replace every occurrence of the variable(s) with its given value. Step 2: Use the order of operations to simplify the resulting expression. Objective 5 Examples Evaluate each expression for the given value(s). 5a. 1 2 x - 5 for x=-4 5b. 4y2 - y + 1 for y = 5 5c. b2 - 4ac for a=-3, b = 2, and c = 5 5d. y2 - y1 x2 - x1 for x1=-2, x2 = 4, y1=-1, and y2=-8 Solutions 5a. 1 2 x - 5 = 1 2 (-4) - 5 Replace x with -4. = -2 - 5 Multiply 1 2 and -4. = -7 Subtract. 5b. 4y2 - y + 1 = 4 (5)2 - (5) + 1 Replace y with 5. = 4 (25) - 5 + 1 Simplify the exponent. = 100 - 5 + 1 Multiply 4 and 25. = 95 + 1 Subtract 5 from 100. = 96 Add. 5c. b2 - 4ac = (2)2 - 4(-3)(5) Replace a with -3, b with 2, and c with 5. = 4 - 4(-3)(5) Simplify the exponent. = 4 + 60 Multiply -4, -3, and 5. = 64 Add. 5d. y2 - y1 x2 - x1 = -8 - (-1) 4 - (-2) -8 + 1 4 + 2 = -7 = 6 or - 7 6 Replace x1 with -2, x2 with 4, y1 with -1, and y2 with -8. Write the numerator and denominator using addition. Add the numbers in the numerator and in the denominator. Student Check 5 Evaluate each expression for the given value(s). a. 1 3 x - 8 for x = 6 b. 2a2 - a + 4 for a=-4 c. -b + 1b2 - 4ac 2a for a = 1, b=-2, and c=-3 d. 1 2 h(b1 + b2) for h = 4, b1 = 3, and b2 = 5
hendricks_intermediate_algebra_1e_ch1_3
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