2. 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
3. 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
4. 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?
5. 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?
6. 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
7. 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 Time Temp
8am 52
Step 3: Write the equation
10am 64
Step 4: Graph the data
12pm 72
2pm 78
Predict the high temperature for the day. 4pm 81
At what time does the nigh temp occur?
6pm 76
