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Word Problems modeled by Quadratic Equations

x + 1. Word Problems modeled by Quadratic Equations. x. Use the 5 Basic Steps to Solve Word Problems. 1. Name what x is. Can only be one thing. when in question choose smaller one. 2. Define everything else in the problem in terms of x. Start with concepts in ENGLISH.

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Word Problems modeled by Quadratic Equations

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  1. x + 1 Word Problems modeled by Quadratic Equations x

  2. Use the 5 Basic Steps to Solve Word Problems 1.Name what x is. • Can only be one thing. • when in question choose smaller one. 2.Define everything else in the problem in terms of x. • Start with concepts in ENGLISH. • Cross out as you go. 3. Write the equation. • Interpret what’s left using dictionary 4.Solve the equation. 5.Answer the question.

  3. Additional Factors... • The “area” of a shape is measured by the number of squares that fit into it. • Quadratics involve squares… x2 • So area problems often end up as quadratic equations. • The area formula for a rectangle is... length • width • The area formula for a triangle is... 1/2(length • width)

  4. Don’t Forget... • Quadratic Equations generally yield two answers. • Length can never be negative. • So only use the positive answers in an area problem.

  5. 3. Write the equation. The width can’t be negative The length of Joe’s kitchen floor is 4 feet more than the width. The area is 117 square feet. What is the length & width ? 1. Name what x is. x = the width 2. Define everything else in the problem. the length = x + 4 x •(x + 4) the area = x •(x + 4) = 117 Area = Length • Width 4. Solve the equation. x2 + 4x = 117 -117 -117 Solve by Factoring x2 + 4x - 117 = 0 (x +13)(x - 9) = 0 5. Answer the question. x = -13 OR 9 The width is 9 (x) The length is 13. (x + 4)

  6. 3. Write the equation. The sum of the squares of 2 consecutive negative integers is 221. What are the 2 numbers ? 1. Name what x is. x = the smaller integer 2. Define everything else in the problem. • the next consecutive integer = x + 1 • square of the smaller integer = x2 • square of the next consecutive integer = (x + 1)2 x2 221 = + (x + 1)2 4. Solve the equation.

  7. x2 221 = + (x + 1)2 x2 221 = + (x + 1)(x + 1) The problem says the answer MUST be negative 4. Solve the equation. = 221 x2 + 2x + 1 x2 + 2x2 + 2x + 1 = 221 -221 -221 Solve by Factoring 2x2 + 2x - 220 = 0 2(x2 + 1x - 110) = 0 2(x+ 11)(x - 10) = 0 x= -11 OR 10 The smaller number is -11 (x) 5. Answer the question. The next consecutive number is -10. (x + 1)

  8. PRACTICE

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