Download y mx b = + y ax bx c = + + y ax bx cx d = + + + y ax bx

Algebra II Pre AP
Notes 12.1 – Analyzing Data
Linear
Name ______________________________________
Date __________________________ Period ______
y  mx  b
Quadratic
Cubic
Quartic
y  ax  bx  c
y  ax  bx  cx  d
y  ax  bx  cx  dx  e
y  a bx
A linear regression is a
line that best fits data
that is either
increasing or
decreasing.
A quadratic regression is a
parabola that best fits
data that increases and
then decreases or
decreases then increases.
A cubic regression best fits
A quartic regression best fits
data that changes direction three
times and the ends of the data
point in the same direction.
Common Difference
Common Difference
Common Difference
An exponential
regression best fits
data that is strictly
increasing or
decreasing at an
increasing or
decreasing rate.
2
3
2
data that changes direction
twice and the ends of the
data point in opposite
directions.
4
3
Exponential
2
Common Difference
Common Ratio
1. Use the scatter plot below. Which of the following equations would be most appropriate to use as a linear model
for the data? Explain.
A) y  4.50 x  88.17
B) y  4.50 x  88.17
C) y  2.09 x 1.34
Solution: B
slope must be negative and y intercept must be positive
2. Analyze the data shown in the scatter plot below. Which of the following equations would be most appropriate to
use as a quadratic model for the data? Explain.
A) y  0.23x2  1.76 x  0.03
B) y  0.23x2  1.76 x  3.82
C) y  0.32 x2  1.22 x  3.82
Solution: A
the a value must be negative and  b  4 , also based on the y intercept
2a
3. Analyze the data shown in the table below. Which of the following equations would be most appropriate to use as
an exponential model for the data? Explain.
A) y  6710(0.56) x  3
B) y  6710(0.56) x
C) y  11981(0.56) x
Solution: C find the approximate y intercept to determine an appropriate a value
4. Use the scatter plot. Which of the following equations would be most appropriate to use as an exponential model
for the data?
A) y  431(0.78) x  2.6
B) y  0.12(1.28) x  431
C) y  431(0.78) x
Solution: C because a > 0 and 0 < b < 1
Use differences or ratios to determine the type of function that best models the data and find the equation.
5.
6.
Quadratic
1
y   x2
4
Linear
y  4 x  3
8. (3, 99), (2, 35),(1, 5),(0,  3),(1,  1),(2,  1),(3,  15)
7.
Exponential
y  2x
Cubic
y   2 x 3  5x 2  x  3
9.
Exponential
y  0.036  2.017 
x
10.
A. linear; y  0.48x
B. quadratic; y  x2  0.48x  18.26
C. exponential; y  0.5(18.3) x
D. linear; y  0.48x  18.26
Solution: D
HW: Textbook Pg. 507 (1 – 11, 14 – 16, 19)