4-3 MODELING WITH QUADRATIC FUNCTIONSChapter 4 Quadratic Functions and Equations

©Tentinger

ESSENTIAL UNDERSTANDING AND OBJECTIVES

Essential Understanding: Three noncollinear points, no two of which are in line vertically, are on the graph of exactly one quadratic function.

Objectives: Students will be able to:

Write the equation of a parabola Apply the quadratic functions to real life

situations Use the quadratic regression function

IOWA CORE CURRICULUM

Functions F.IF.4. For a function that models a

relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F.IF.5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationships it describes

WRITING AN EQUATION OF PARABOLA

A parabola contains the points (0, 0), (-1, -2), and (1, 6). What is the equation of this parabola in standard form?

Step 1: Write a system of equations by substituting the coordinates in to the standard form equation

Step 2: Solve the system of equations to find the variables

Step 3: Substitute the solutions into the standard form equation

A parabola contains the points (0, 0), (1, -2), and (-1, 4). What is the equation of this parabola in standard form?

USING A QUADRATIC MODEL

A player throws a basketball toward the hoop. The basketball follows a parabolic path through the points (2, 10), (4, 12), and (10, 12). The center to the hoop is at (12, 10). Will the ball pass through the hoop?

What do the coordinates represent?

EXAMPLE

The parabolic path of a thrown ball can be modeled by the table. The top of the wall is at (5, 6). Will the ball go over the wall on the way up or the way down? What is the domain and range of this graph?

x y

1 3

2 5

3 6

QUADRATIC REGRESSION:

When more than three points suggest a quadratic function, you use the quadric regression feature of a graphing calculator to find a quadratic model.

The table shows a meteorologists predicted temp for an October day in Sacramento, CA.

Step 1: enter the data into the list function on your calc. (how do you think you should represent time? Why?)

Step 2: Use the QuadReg function under STAT

Step 3: Write the equation Step 4: Graph the data

Predict the high temperature for the day. At what time does the nigh temp occur?

Time Temp

8am 52

10am 64

12pm 72

2pm 78

4pm 81

6pm 76

HOMEWORK

Pg. 212 – 213 # 8 – 16 even, 17, 18, 22, 25, 26 10 problems