QUADRATIC RELATIONS
(An Introduction)
Example 
The graph shows a soccer ball’s height above the ground over time
after it was kicked in the air.
a) Describe the shape of the graph.
b) What was the ball’s maximum height?
c) How long was the ball in the air?
vertex:
is the point at which the graph changes from decreasing
to increasing or from increasing to decreasing
A parabola always has a minimum or maximum value
(the y-coordinate of the vertex).
CASE 
If the parabola opens up there
will be a minimum value.
Unit 2 Lesson 1
CASE 
If the parabola opens down there
will be a maximum value.
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Example 
The table shows how two variables,
x and y, are related.
x
y
0
1
2
3
4
5
6
1
6
9
10
9
6
1
First
Differences
a)
Calculate the first and second differences.
b)
Is the relation linear or quadratic?
degree:
Second
Differences
_________________________
the degree of a polynomial with a single variable is
the value of the highest exponent of the variable
Example 
Which of the
relations are
quadratic?
a)
y = 4x – 5
Degree?
_____
b)
y = 2x2 + 5x – 8
Degree?
_____
SUMMARY To identify a quadratic function:
Quadratic Functions
Table of Values
Graph
Equation
Unit 2 Lesson 1
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THE BASIC PARABOLA
Sketch the graph of y = x2 using the given table of values:
x
-3
-2
-1
0
1
2
3
y
ordinate differences:
the differences in the
y-coordinates
V(0,0)
OD: 1, 3, 5, …
y
x
Homework: p.174–175 #1abe, 2, 3a, 4
Unit 2 Lesson 1
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