Solving Word Problems Involving Quadratic Equations

Solving Word Problems Involving Quadratic Equations

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  Solving Word ProblemsInvolving Quadratic Equations
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  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
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  How do wesolve 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
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  Practice p. 774-77510,12 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
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  How do wesolve 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
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  How do wesolve area problems? (what is the formula for area of a rectangle? Draw diagram Label information Write formula Substitute and solve
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  The length ofa 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