Do Now

• Pass out calculators. • You have about 10 minutes to

work on your EOC Packet.

Objective:

• To compare linear, exponential, and quadratic models.

Choose functions using sets of ordered pairsEXAMPLE 1

Use a graph to tell whether the ordered pairs represent a linear function, an exponential function, or a quadratic function.

a. – 4,1

32 0,

1 2

– 2,18

2, 2 4, 8,, , ,

a.

Exponential function

SOLUTION

Choose functions using sets of ordered pairs

EXAMPLE 1

b.

Linear function

b. – 4, 1 , –2, 2 , 0, 3 , 4, 52, 4 ,

Choose functions using sets of ordered pairs

EXAMPLE 1

,c. –4, 5 , –2, 2 , 0, 1 , 4, 52, 2 ,

c.

Quadratic function

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. Extend the table to find the y-value for the next x-value.

ANSWER

The table of values represents a quadratic function. When x = 3, y = 6 + 8 = 14.

x –2 –1 0 1 2

y –6 –6 –4 0 6

First differences: 0 2 4 6

Second differences: 2 2 2

a.

Identify functions using differences or ratiosEXAMPLE 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.

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

Write an equation for a functionEXAMPLE 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 functionEXAMPLE 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

Write an equation for a functionEXAMPLE 3

STEP 2 Write an equation for the quadratic function. The equation has the form y = ax2. Find the value of a by using the coordinates of a point that lies on the graph, such as (1, 0.5).

y = ax2 Write equation for quadratic function.

0.5 = a(1)2 Substitute 1 for x and 0.5 for y.

0.5 = a Solve for a.

The table of values represents a quadratic function because the second differences are equal.

Write an equation for a functionEXAMPLE 3

ANSWER

The equation is y = 0.5x2.

CHECK

Plot the ordered pairs from the table. Then graph y = 0.5x2 to see that the graph passes through the plotted points.

EXAMPLE 3GUIDED PRACTICE

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 –3 –2 –1 0 1

y –7 –5 –3 –1 1

3.

for Example 3

ANSWER

linear function, y = 2x 1

EXAMPLE 3GUIDED PRACTICE for Example 3

x –2 –1 0 1 2

y 8 2 0 2 8

4.

Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. Then write an equation for the function.

ANSWER

quadratic function, y = 2x2

Exit Ticket - Poster

• Pg. 688 # 2, 13 – 15 odd