do now pass out calculators. you have about 10 minutes to work on your eoc packet
TRANSCRIPT
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