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

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

3. Additional Factors... The “area” of a shape is measured by the number of squares that fit into it. Quadratics involve squares… x 2 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. 1. Name what x is. 2. Define everything else in the problem. 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 ? x = the width the length = x + 4 3. Write the equation. x (x + 4) = 117 the area = x (x + 4) Area = Length Width 4. Solve the equation. x 2 + 4x = 117 -117 x 2 + 4x - 117 = 0 Solve by Factoring (x +13)(x - 9) = 0 x = -13 OR 9 5. Answer the question. The width is 9 (x) The width can’t be negative The length is 13. (x + 4)

6. 1. Name what x is. 2. Define everything else in the problem. The sum of the squares of 2 consecutive negative integers is 221. What are the 2 numbers ? x = the smaller integer ­ the next consecutive integer = x + 1 3. Write the equation. x2x2 = ­ square of the smaller integer = x 2 ­ square of the next consecutive integer = (x + 1) 2 +(x + 1) 2 221 4. Solve the equation.

7. x2x2 = +(x + 1) 2 2214. Solve the equation. x2x2 = +(x + 1)(x + 1) 221 x 2 + x 2 + 2x + 1 = 221 2x 2 + 2x + 1 = 221 -221 2x 2 + 2x - 220 = 0 Solve by Factoring 2(x 2 + 1x - 110) = 0 2(x + 11)(x - 10) = 0 x = -11 OR 10 5. Answer the question. The problem says the answer MUST be negative The smaller number is -11 (x) The next consecutive number is -10. (x + 1)

8. PRACTICE