PRE-AP PRE- CALCULUS CHAPTER 2, SECTION 1 Linear and Quadratic Functions and Modeling

Polynomial Functions

Which of the following are polynomial functions? If they are, state the degree and leading coefficient.

Polynomial Functions of No and Low Degree NameFormDegree Zero functionUndefined Constant Function 0 Linear Function1 Quadratic Function 2

Provide Examples of the following: Zero Function: Constant Function: Linear Function: Quadratic Function:

Linear Function

Average Rate of Change

Camelot Apartments bought a $50,000 building and for tax purposes are depreciating it $2000 per year over a 25-yr period using straight-line depreciation. What is the rate of change of the value of the building? Write an expression for the value v(t) of the building as a linear function of the time t since the building was placed in service. Evaluate v(0) and v(16). Solve v(t) = 39,000

Linear Correlation and Modeling

Use the data in the table to write a linear model for demand (in the boxes sold per week) as a function of the price per box (in dollars). Weekly Sales Data Based on Marketing Research Price Per boxBoxes Sold $2.4038,320 $2.6033,710 $2.8028,280 $3.0026,550 $3.2025,530 $3.4022,170 $3.6018,260

What are the steps for plotting a scatterplot in the calculator, then finding the equation of the line?

Quadratic Functions & Their Graphs A quadratic function is a polynomial function of degree ____. The graph of the squaring function _________ is a _____________. The parent function of any upward- or downward-opening parabola is ___________.

Standard Quadratic Formula

Find the zeros of the function.

Find the roots of the function

Comparing Standard Form & Vertex Form

Vertex Form

The nature of a Quadratic function Point of ViewCharacterization VerbalPolynomial of degree 2 Algebraic Graphical

Application of Quadratics Julie Stone designed a rectangular patio that is 25 ft by 40 ft. This patio is surrounded by a terraced strip of uniform with small trees and shrubs. If the are A of this terraced strip is 504 square feet, find the width x of the strip.

Application of Quadratics

Vertical Free Fall of Motion

Vertical Free Fall Application As a promotion for the Houston Astros downtown ballpark, a competition is held to see who can throw a baseball the highest from the front row of the upper deck of seats, 83 ft above field level. The winner throws the ball with an initial vertical velocity of 92 ft/sect and it lands on the infield grass. a) Find the maximum height of the baseball. b) How much time is the ball in the air? c) Determine its vertical velocity when it hits the ground.

Critical Thinking: Write an equation for the linear function f such that f(-1)=2 and f(3)=-2.

Critical Thinking: Write an equation for the linear function f such that f(0)=3 and f(3)=0.

Homework for Chapter 2.1 Page : #’s 2, 9, 12, 13, 16, 22, 24, 25, 27, 40, 45, 47, 66, 75, 78 (a & b) (total of 15 problems)