Pre-Calculus Honors Unit 3 Lesson 1
Pre-calculus (H)
Date:
Book Reference 2.1
Unit 3 Lesson 1: Applications of Polynomials (Focusing on Quadratics)
Objective: _______________________________________________________
Do Now: Answer the following questions, given, f (x) = -2x 2 - 4x +1, without a graphing calculator.
a.) Determine whether the graph opens up or down? Explain.
b.) Does this graph have a maximum or minimum? State where the maximum or minimum occurs.
c.) Find the range of the function.
Problem #1: Using Quadratics to Find Maximum Area
Verbal Representation
Directions: Mark up the following word
problem.
Diagram
Directions: Draw a diagram that represents the verbal.
You are building a rectangular pen with
three parallel dividers using 500 feet of
fencing.
What dimensions will maximize the
total area of the pen? ___________
What is the maximum area enclosed?
____________
Algebraic
Directions: Use the following steps to
create an area function in terms of x.
1. Define your variables.
x: ________________________________
Graph
Directions: Graph A(x) using a graphing calculator. Sketch
the graph of the function below. Label your vertex and xintercepts. State your viewing window in the space
provided.
y: ________________________________
Window Dimensions
x min:
2. Create an equation that represents the
amount of fencing that is used in terms of x
and y.
x max:
x scl:
3. Create an area function A(x), in terms of x,
by solving the equation in #2 for y, and
substituting that expression into the area
formula.
y min:
y max:
y scl:
Pre-Calculus Honors Unit 3 Lesson 1
Problem #2:Using Quadratics in the Real World
Verbal Representation
Diagram
Directions: Mark up the following word Directions: Draw a diagram that represents the
problem.
verbal.
A large painting in the style of Rubens
is 3 feet longer than it is wide. If the
wooden frame is 12 inches wide and the
area of the picture and frame is 208
square feet, find the dimensions of the
painting.
Algebraic
Graph
1. Create an equation that represents
the area of the painting and frame.
Directions: Solve the equation you created graphically
below, using a graphing calculator. State your viewing
window in the space provided.
2. Solve the equation algebraically to
find the dimensions of the painting.
Window Dimensions
x min:
x max:
x scl:
y min:
y max:
y scl:
Pre-Calculus Honors Unit 3 Lesson 1
Problem #3: Using Quadratics in the Real World
Verbal Representation
Directions: Mark up the following
word problem.
Diagram
Directions: Draw a diagram that represents the
verbal.
Julie Stone designed a rectangular
patio that is 25 feet by 40 feet. A
terraced strip, of uniform width,
surrounds the patio. If the area of
this terraced strip is 504 square feet,
find the width of the strip.
Algebraic
1. Create an equation that
represents the area of the
terrace.
Graph
Directions: Solve the equation you created graphically
below, using a graphing calculator. State your viewing
window in the space provided.
Window Dimensions
x min:
2. Solve the equation algebraically
to find the width of the strip.
x max:
x scl:
y min:
y max:
y scl:
Pre-Calculus Homework: Continue to work on any problems that were not
completed during the allowed class time.