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2.8 Quadratic Applications Word Problems OK: We are going to split into two groups: The 9th grade vs. the 10th grade… ooooooh! You each will get a quadratic word problem to solve. The goal is to determine A) What you are actually being asked to find and B) How to solve the problem. Then we will compare and see if you agree Word Problems? AUGH!!!! RELAX!! Problem 1: The sum of a number and its square is 132. Find the number. Problem 2: I have 80 feet of fence to make a garden which will have one wall of my house as a border. Find the dimensions so that the area is a maximum. What is going on here? These are quadratic word problems. 1. There will be enough information for 2 equations with 2 unknowns. 2. The equation setup will involve multiplication or squaring; it won’t be linear systems. 3. You will be asked either to solve (i.e. set = 0) or find x so as to maximize or minimize the situation. Maximize? Minimize Why would we be talking about maximizing or minimizing with quadratic word problems? Quadratic? Maximize? What are we looking for? Oh yeah! The vertex!! Examples 2. Find two consecutive positive integers such that the sum of their squares is 113. (notice! No “maximum/minimum”) 3. The sum of two numbers is 40. Find the two numbers if their product is a maximum. 4. The sum of a number and its square is 72. Find the number. Examples 5. The sum of 2 numbers is 12. Find the numbers if the product of one and twice the other is a maximum. 6. The length of a rectangle is 3 cm greater than the width. The area is 70 square centimeters. Find the dimensions. Reminders: 1. There will be enough information for 2 equations with 2 unknowns. 2. The equation setup will involve multiplication or squaring; it won’t be linear systems. 3. You will be asked either to solve (i.e. set = 0) or find x so as to maximize or minimize the situation. Homework will be changed: