1. 10.8 Compare Linear, Exponential, and Quadratic Models

2. 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

3. Examples: LINEAR, QUADRATIC or EXPONENTIAL? y = 6x + 3 y = 7x2 +5x – 2

4. Identifying from a graph:
Linear Makes a straight line
Quadratic Makes a U or ∩
Exponential Rises or falls quickly in one direction

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

6. Is the table linear, quadratic or exponential?
y changes more quickly than x.
Never see the same y value twice.
Common multiplication pattern
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

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

8. 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 –2 –1 1 2 y –6 –4 6
First differences:
Second differences:
ANSWER
The table of values represents a quadratic function.

9. 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. y 2 x
– 2
– 1 1
0.08
0.4 10
ANSWER
exponential function

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

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

12. 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 1 2 y
0.5

13. EXAMPLE 3
Write an equation for a function
SOLUTION
STEP 1
Determine which type of function the table of values represents. x –2 –1 1 2 y
0.5
First differences: – –
Second differences: