Quadratic Functions(features and charecteristics).ppt

Warm-up
1. Graph y = 3x
.
ANSWER
Tell whether the ordered pairs (0, 0), (1, 2), (2, 4),
and (3, 6) represent a linear function.
2.
For y = x2
– 3x – 5, find corresponding y-values for
the x-values –2, 1, and 3.
3.

10.8 Compare Linear, Exponential,
and Quadratic Models
•Students will Compare Linear, Exponential,
and Quadratic Models

Identifying from an equation:
Linear
Has an x with
no exponent.
y = 5x + 1
y = ½x
2x + 3y = 6
Quadratic
Has an x2
in the
equation.
y = 2x2
+ 3x – 5
y = x2
+ 9
x2
+ 4y = 7
Exponential
Has an x as
the
exponent.
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
Makes a
straight line
Quadratic
Makes a U or ∩
Exponential
Rises or falls
quickly in
one direction

LINEAR, QUADRATIC or EXPONENTIAL?
a) b)
c) d)

Is the table linear, quadratic or
exponential?
Quadratic
• See same y
more than
once.
• 2nd
difference
is the same
Linear
• Never see
the same y
value twice.
• 1st
difference
is the same
Exponential
• y changes
more quickly
than x.
• Never see
the same y
value twice.
• Common
multiplication
pattern

Identify functions using differences or ratios
EXAMPLE 2
ANSWER
The table of values represents a linear function.
x – 2 – 1 0 1 2
y – 2 1 4 7 10
Differences: 3 3 3 3
b.

Identify functions using differences or ratios
EXAMPLE 2
Use differences or ratios to tell whether the table of
values represents a linear function, an exponential
function, or a quadratic function.
ANSWER
The table of values represents a quadratic function.
x –2 –1 0 1 2
y –6 –6 –4 0 6
First differences: 0 2 4 6
Second differences: 2 2 2
a.

GUIDED PRACTICE for Examples 1 and 2
2. Tell whether the table of values represents a
linear function, an exponential function, or a
quadratic function.
ANSWER exponential function
0
y 2
x – 2 – 1 1
0.08 0.4 10

x y
0 -5
1 -4
2 -1
3 4
4 11
x y
-2 -2
-1 -4
0 -8
2 -32
5 -256

Is the table linear, quadratic or
exponential?
x y
1 0
2 -1
3 0
4 3
5 8
x y
1 5
2 9
3 13
4 17
5 21
x y
1 3
2 9
3 27
4 81
5 243

Write an equation for a function
EXAMPLE 3
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

SOLUTION
Write an equation for a function
EXAMPLE 3
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 –0.5 0.5 1.5
Second differences: 1 1 1

Quadratic Functions(features and charecteristics).ppt

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