MINDS ON!!
The table shows a soccer ball's height (m) above the ground over
time (s) after it as kicked in the air.
time (s) height (m)
0
1.10
0.5
7.80
1.0
12.00
1.5
13.80
2.0
13.00
2.5
9.75
3.0
4.00
Words of the day:
a) Graph the data and draw a smooth curve
through the points.
b) Describe the shape of the graph.
c) What was the ball's maximum height?
d) For about how many seconds was the ball in the air?
First Differences – the differences between the y­values that correspond to
consecutive x­values (rate of change)
Second Differences – the difference between consecutive first differences
Example 1: Make a table of values, then determine the first and second
differences.
a) y = 3x − 1
4.1 Investigate Non-Linear Relations
b) y = ­x2 ­ 2x + 1
Is it linear or non-linear?
Example 2:
Identify whether each relation is linear, quadratic, or neither.
Quadratics (Non-linear)
First differences are
___________
Second differences are
_____________
The graph is a _______
of best fit
Lines (Linear)
a)
b)
First differences are
___________
The graph is a __________
of best fit
The equation has degree
________
The equation has degree
________
Summary of Linear vs. Non-linear Relations
Linear
Non- Linear
Homework:
p. 166 # 1, 2, 3
pp. 172-173 # 3, 9