Download 10.8 Compare Linear, Exponential, and Quadratic Models

Big Ideas
Lesson 8.6B
10.8 Compare Linear, Exponential,
and Quadratic Models
•Students will Compare Linear, Exponential,
and Quadratic Models
Identifying from an equation:
Linear
Quadratic
Exponential
Has an x with
no exponent.
Has an x2 in the
equation.
Has an x as
the exponent.
y = 5x + 1
y = ½x
2x + 3y = 6
y = 2x2 + 3x – 5
y = x2 + 9
x2 + 4y = 7
y = 3x + 1
y = 52x
4x + y = 13
Examples:
• LINEAR, QUADRATIC or EXPONENTIAL?
a)y = 6x + 3
b)y = 7x2 +5x – 2
c)9x + 3 = y
d)42x = 8
Identifying from a graph:
Linear
Quadratic
Exponential
Makes a
straight line
Makes a U or ∩
Rises or falls
quickly in one
direction
LINEAR, QUADRATIC or EXPONENTIAL?
a)
b)
c)
d)
Is the table linear, quadratic or
exponential?
Linear
• Never see the
same y value
twice.
• 1st difference
is the same
Quadratic
• See same y
more than
once.
• 2nd difference
is the same
Exponential
• y changes
more quickly
than x.
• Never see the
same y value
twice.
• Common
multiplication
pattern
EXAMPLE 2
b.
Identify functions using differences or ratios
x
–2
–1
0
1
2
y
–2
1
4
7
10
Differences:
3
3
3
3
ANSWER
The table of values represents a linear function.
EXAMPLE 2
Identify functions using differences or ratios
Use differences or ratios to tell whether the table of
values represents a linear function, an exponential
function, or a quadratic function.
a.
x
y
–2
–6
First differences: 0
Second differences: 2
–1
–6
0
–4
2
1
0
4
2
2
6
6
2
ANSWER
The table of values represents a quadratic function
.
GUIDED PRACTICE
2.
for Examples 1 and 2
Tell whether the table of values represents a
linear function, an exponential function, or a
quadratic function.
ANSWER
x
–2
–1
0
1
y
0.08
0.4
2
10
exponential function
x
y
x
y
0
-5
-2
-2
1
-4
-1
-4
2
-1
0
-8
3
4
2
-32
4
11
5
-256
Is the table linear, quadratic or
exponential?
x
y
x
y
x
y
1
5
1
0
1
3
2
9
2
-1
2
9
3
13
3
0
3
27
4
17
4
3
4
81
5
21
5
8
5
243
EXAMPLE 3
Write an equation for a function
Tell whether the table of values represents a linear
function, an exponential function, or a quadratic
function. Then write an equation for the function.
x
–2
–1
0
1
2
y
2
0.5
0
0.5
2
EXAMPLE 3
Write an equation for a function
SOLUTION
STEP 1 Determine which type of function the table of
values represents.
x
–2
–1
0
1
2
y
2
0.5
0
0.5
2
First differences: –1.5
Second differences: 1
–0.5
0.5
1
1.5
1