Algebra 1
Name: _______________________________
Unit 6: Lesson 8
Date: _________________ Period: _______
Notes… Applications Factoring and Solving Quadratics
Essential Questions:
 Why is factoring necessary?
Goal:
 Students will solve real-world applications that involve quadratic equations and factoring.
Strategies:
1) Define your variables (Set-up the “let statement”)
2) Identify the information in the problem appropriately…
a. What are you GIVEN ?
b. What is the UNKNOWN ?
3) Read the last sentence twice
a. This is usually where the problem tells you what you are expected to find.
4) Check your answers…
a. Are your answers mathematically correct?
b. Do your answers make sense? Are they reasonable?
5) LABEL, LABEL, LABEL!
1) Consider a rectangle of one side of length x  6 and having an area given by A  x 2  17 x  66 .
A) Find an expression for the other side of the rectangle.
B) If the area of the rectangle is 84 square feet, what are the possible values for x?
C) For the value of x found in part B, determine the dimensions of the rectangle.
2) A 15-foot ladder is leaning against the side of a house. The top of the ladder reaches up the house three feet
more than the distance the base of the ladder is from the bottom of the house. How high up the side of the
house does the ladder reach?
3)
A) Diagram:
B) Work:
C) Solution:
D) Check:
If the sides of a square are increased by 3 meters, the area becomes 64 meters2. Find the perimeter of the
original square.
A) Diagram:
B) Work:
C) Solution:
D) Check:
4) The product of two consecutive negative, odd integers is 3. Find the two integers.
A) Diagram:
B) Work:
C) Solution:
D) Check:
5) You have made a rectangular stained glass window that is 2 feet by 4 feet. You have 7 square feet of clear glass
to create a border of uniform width around the window. What should the width of the border be?
Diagram:
B) Work:
C) Solution:
D) Check:
6)
7)
If you throw a ball straight up from the ground with an initial velocity of 64 feet per second, will the ball reach a
height of 64 feet? If it does, how long will it take to reach that height? Use the following vertical motion model
h  16t 2  64t .
A) Diagram:
B) Work:
C) Solution:
D) Check:
Suppose a diver jumps from a ledge that is 48 feet above the ocean and the initial upward velocity is 8 feet per
second. The vertical motion of the diver can be modeled by the function h  16t 2  8t  48 . How long will it
take until the diver enters the water?
A) Diagram:
B) Work:
C) Solution:
D) Check:
8) The length of a rectangle is 3cm more than the width. The area is 70 cm2. Find the dimensions of the rectangle.
A) Diagram:
B) Work:
C) Solution:
D) Check:
9) You are putting a stone border along two consecutive sides of a rectangular garden that measures 6 yards by 15
yards. Your budget limits you to only enough stone to cover 46 square yards. How wide should the border be?
A) Diagram:
B) Work:
C) Solution:
D) Check:
10) Picasso creates a painting on a rectangular canvas with a width that is 6 inches longer than the height, as
shown in the diagram below.
h
h+6
A)
Write a polynomial expression, in simplified form, that represents the area of the canvas.
B)
Picasso adds a 4-inch-wide frame around all sides of his canvas. Write a polynomial expression, in
simplified form, that represents the total area of the canvas and the frame.
C)
Picasso is unhappy with his 4-inch-wide frame, so he decides to put a frame with a different width
around his canvas. The total area of the canvas and the new frame is given by the polynomial
h 2  12h  27 , where h represents the height of the canvas. Determine the width of the new
frame.