2.8 Quadratic Applications

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2.8 Quadratic Applications

• Word Problems

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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

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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.

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What is going on here?

• These are quadratic word problems.
• There will be enough information for 2 equations
  with 2 unknowns.
• The equation setup will involve multiplication or
  squaring it wont be linear systems.
• You will be asked either to solve (i.e. set 0)
  or find x so as to maximize or minimize the
  situation.

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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!!

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Examples

1. Find two consecutive positive integers such that
   the sum of their squares is 113. (notice! No
   maximum/minimum)
2. The sum of two numbers is 40. Find the two
   numbers if their product is a maximum.
3. The sum of a number and its square is 72. Find
   the number.

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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.

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Reminders

1. There will be enough information for 2 equations
   with 2 unknowns.
2. The equation setup will involve multiplication or
   squaring it wont 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