Transcript QUADRATIC FUNCTIONS

SECTION 2.2
BUILDING LINEAR FUNCTIONS
FROM DATA
LINEAR CURVE FITTING
STEP 1: Ask whether the
variables are related to each
other.
STEP 2: Obtain data and verify a
relation exists. Plot the points to
obtain a scatter diagram.
STEP 3: Find an equation which
describes this relation.
FINDING AN EQUATION FOR
LINEARLY RELATED DATA
A farmer collected the following
data, which shows crop yields for
various amounts of fertilizer
used.
Fertilizer (X lbs)
Yield (Y bushels)
0
4
0
6
5
10
5
7
10
12
10
10
15
15
15
17
20
18
20
21
25
23
25
22
GETTING A SCATTER
PLOT OF THE DATA
Ensure that all equations in the Y=
menu are cleared out or disabled.
Input the data into the lists in the
statistics editor: STAT 1:Edit
Turn on a Statistics Plotter and set the
desired parameters: 2nd Y=
Push Zoom and choose ZoomStat.
GETTING A LINE OF
BEST FIT
Verify by the scatter plot that the data
has a linear relationship.
Go to the home screen, press STAT,
arrow to CALC, and choose LinReg.
A linear regression equation will
appear in the home screen.
GRAPHING THE
REGRESSION EQUATION
To put the regression equation in the Y=
menu:
1. Push Y=
2. Push VARS, choose Statistics,
arrow to EQ, and choose
RegEQ.
Now push GRAPH.
MAKING A PREDICTION
Use the Linear Regression Equation to
Estimate the Yield if the farmer uses 17
pounds of fertilizer.
1.
Go to home screen
2.
Go into YVARS, choose Function,
Choose Y1.
3.
Type in (17).
MAKING A PREDICTION
Our prediction is that the crop yield for
17 Pounds of fertilizer per 100 ft2 will
be
17 Bushels
CONCLUSION OF SECTION 2.2
VARIATION
Relationships between variables are
often described in terms of
proportionality.
For Example:
Force is proportional to acceleration.
Pressure and volume of an ideal gas are
inversely proportional.
DIRECT VARIATION
Let x and y denote two quantities. Then
y varies directly with x, or y is directly
proportional to x, if there is a nonzero
number k such that
y = kx
constant of proportionality
EXAMPLE
For a certain gas enclosed in a
container of fixed volume, the pressure
P (in newtons per square meter) varies
directly with temperature T (in kelvins).
If the pressure is found to be 20
newtons/m2 at a temperature of 60 K,
find a formula that relates pressure P to
temperature T. Then find the pressure
P when T = 120 K.
SOLUTION
First, we know that P varies directly
with T.
P=kT
And, we know P = 20 when T = 60.
Thus, 20 = k(60)
1
k 
3
SOLUTION
The formula, then, is
1
P
T
3
Now, we must find P when T = 120K
1
P
(120)
3
P = 40 newtons per square meter