Transcript 2.8 Quadratic Applications

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: