2.8 Quadratic Applications - PowerPoint PPT Presentation

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2.8 Quadratic Applications

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You each will get a quadratic word problem to solve. ... The equation setup will involve multiplication or squaring; it won t be linear systems. – PowerPoint PPT presentation

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Title: 2.8 Quadratic Applications


1
2.8 Quadratic Applications
  • Word Problems

2
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

3
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.

4
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.

5
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!!

6
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.

7
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.

8
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
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