Solving Word Problems Involving Quadratic Equations
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This document provides instructions for solving word problems involving quadratic equations. It explains how to write let statements and equations, solve for consecutive integers or areas, and check solutions. Sample problems are worked through, such as finding two consecutive integers whose sum is 13, or the dimensions of a rectangular garden with an area of 27 square units.
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Solving Word Problems Involving Quadratic Equations
- 1. Solving Word Problems Involving Quadratic Equations
- 2. Do Now: Write a “let” statement and equation for each example. Explain the difference. Find two consecutive integers whose sum is 13. Let x = first integer x + 1 = second integer x + x + 1 = 13 Find two consecutive integers whose product is 42. Let x = first integer x + 1 = second integer x(x + 1) = 42
- 3. How do we solve consecutive integer problems? Write “let” statement (if consecutive integers, use x;x+1;x+2. If consecutive even or odd, use x;x+2:x+4) Write equation using key words from statement: sum (add), product (multiply), more than (add), less than (subtract), etc. Solve equation Check in original problem statement
- 4. Practice p. 774-775 10,12 Let x = first odd integer x + 2 = second odd integer x(x + 2) = 143 x 2 + 2x = 143 x 2 + 2x – 143 = 0 (x + 13)(x – 11) = 0 x = - 13 x = 11 Integers: -13 and – 11 11 and 13 Let x = first integer x + 1 = second integer x + 2 = third integer (x + 1)(x + 2) = 30 x 2 + 3x + 2 = 30 x 2 + 3x – 28 = 0 (x + 7)(x – 4) = 0 x = - 7 x = 4 Integers: -7, - 6, - 5 4, 5, 6
- 5. How do we solve word problems? Practice p. 774 #2 Let x = the number x 2 – 9x = 36 x 2 – 9x – 36 = 0 (x – 12)(x + 3) = 0 x – 12 = 0 x + 3 = 0 x = 12 x = - 3
- 6. How do we solve area problems? (what is the formula for area of a rectangle? Draw diagram Label information Write formula Substitute and solve
- 7. The length of a rectangular garden is 6 more than the width. The area is 27 sq. units. Find the dimensions of the garden. x(x + 6) = 27 x 2 + 6x = 27 x 2 + 6x – 27 = 0 (x + 9)(x – 3) = 0 x + 9 = 0 x – 3 = 0 x = - 9 x = 3 REJECT Dimensions: 3, 9