Download Section 8.4 (6.7)

8.4
Graphs of Quadratic Equations and Functions
1. Identify the domain and range of a relation and
determine if the relation is a function.
2. Find the value of a function.
3. Graph functions.
6.7
Functions and Graphing
1. Graph quadratic equations in the form
y = ax2 + bx + c.
2. Graph quadratic functions.
Relation:
A set of ordered pairs.
Domain:
The set of all input values (x-values) for a
relation.
Range:
The set of all output values (y-values) for a
relation.
Function: A relation in which every value in the
domain is paired with exactly one value in
the range.
Identify the domain and range and tell if it is a
function.
{(−4, −1), (−2, 1), (0, 0), (2, −1), (4, 2)}
Domain:
{-4, -2, 0, 2, 4}
Range:
{-1, 1, 0, 2}
Function:
Yes
Identify the domain and range and tell if it is a
function.
Domain:
(-∞, ∞)
Range:
[-2, ∞)
Function:
Yes
Find f(-3) for
f x   x  4  2
f  3   3  4  2
 7 2
72
9
3
Graph: f  x   x  2
4
y - intercept : 0,2
3
Slope :
4
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Quadratic equation in two variables: An equation that
can be written in the form y = ax2 + bx + c, where a, b,
and c are real numbers and a  0.
Shape: Parabola
Axis of symmetry: A line that divides a graph
into two symmetrical halves.
Vertex: The lowest point on a
parabola that opens up or the
highest point on a parabola that
opens down.
axis of symmetry
x = 0 (y-axis)
Function: Yes
vertex
(0, 0)
Graph.
f(x) = 2x2
x
f(x)
2
8
1
2
0
0
1
2
2
8
f  x   3x  4
2
Graph.
x
f(x)
2
-8
1
1
0
4
1
1
2
-8
Opening of a Parabola
For
y = ax2 + bx + c
a > 0: opens upward
a < 0, opens downward
Graph.
f(x) = | x |
x
f(x)
2
2
1
1
0
0
1
1
2
2
Graph.
f(x) = | x – 1 | + 3
x
f(x)
2
6
1
5
0
4
1
3
2
4
f x  x
Graph.
x
f(x)
0
0
1
1
4
2
9
3
16
4
Library of Functions
f  x   mx  b
f x  x
2
When an equation in one variable is solved the answer is a point on a line.
f x  x
f x  x
Which could be the graph of f  x   x
a)
b)
c)
d)
Copyright © 2011 Pearson Education, Inc.
2
Slide 3- 15
Which could be the graph of f  x   x
a)
b)
c)
d)
Copyright © 2011 Pearson Education, Inc.
2
Slide 3- 16
Which could be the graph of f  x   x
a)
b)
c)
d)
Copyright © 2011 Pearson Education, Inc.
Slide 3- 17
Which could be the graph of f  x   x
a)
b)
c)
d)
Copyright © 2011 Pearson Education, Inc.
Slide 3- 18