Transcript Let`s Get Ready to Play Some

Let’s Get Ready
To Play Some . . .
JEOPARDY
JEOPARDY
JEOPARDY
Jeopardy Board
Final Jeopardy
Solve Quadratic
Equations
Roots
Analyze
Parabolic
Graphs
100
100
100
100
200
200
200
200
300
300
300
300
400
400
400
400
500
500
500
500
Problem Solving
Solve Quadratic Equations 100
What is the solution set for the equation
3x2 – 4x +1 = 0?
Board
Answer
Solve Quadratic Equations 100
What is the solution set for the equation
3x2 – 4x +1 = 0?
1

A 1, 
3

 11 11 
B  , 
 6 6
 8 8
C  , 
 6 6
 1
D 1, 
 3
Board
Algebra
Factor 3x2 – 4x + 1
( 3x – 1 )( x – 1 ) = 0
Set each factor = 0
3x – 1 = 0 and x – 1 = 0
+1 +1
+1 +1
3x = 1
x =1
3
3
1
x
3
Graphing
Solve Quadratic Equations 200
The polynomial x2 + x − 6 is modeled
below using algebraic tiles.
What are the solutions to the equation x2 + x = 6?
Board
Answer
Solve Quadratic Equations 200
The polynomial x2 + x − 6 is modeled
below using algebraic tiles.
What are the solutions to the equation x2 + x = 6?
A
B
C
D
x = −3 and x = −2 First, set equal to zero
x2 + x = 6
x = −3 and x = 2
Set each factor = 0
–6 –6
x = 3 and x = −2
x2 + x – 6 = 0
x + 3 = 0 and x – 2 = 0
x = 3 and x = 2
–3 –3
+2 +2
Factor x2 + x – 6
Board
x =2
x
=
-3
( x + 3 )( x – 2 ) = 0
Solve Quadratic Equations 300
What is the solution set for the equation
4(3x − 2)2 = 36
Board
Answer
Solve Quadratic Equations 300
What is the solution set for the equation
First, set equal to zero
4(3x − 2)2 = 36
4(3x − 2) = 36
2
A
B
C
D
11
{− 6 ,
11
{− 3 ,
1
{− 3,
2
{− 3 ,
Board
11
}
6
11
}
3
5
}
3
4
}
3
–36 –36
4(3x − 2)2 – 36 = 0
ENTER
ENTER
ENTER
2nd QUIT
2nd ANS (-)
Solve Quadratic Equations 400
Nancy threw a ball upward from the roof of a 50-foot-high building at an
initial velocity of 40 feet per second. The table shows the relationship
between the time elapsed and the ball’s height above the ground.
If the height of the ball is a quadratic function of time,
between what times did the ball reach a height of 70 ft
Board
Answer
Solve Quadratic Equations 400
Nancy threw a ball upward from the roof of a 50-foot-high building at an
initial velocity of 40 feet per second. The table shows the relationship
between the time elapsed and the ball’s height above the ground.
If the height of the ball is a quadratic function of time,
between what times did the ball reach a height of 70 ft
F
G
H
J
Between 0 and 0.5 sec.
Between 1 and 1.5 sec.
Between 0.5 and 1 sec. and 1.5 and 2 sec.
Between 1 and 1.5 sec. and 1.5 and 2 sec.
Path of the ball
Board
Height of 70
It occurs twice
Solve Quadratic Equations 500
The completion of a certain chemical reaction is
expressed by the equation y = 250 − 5x − x2, where
y is the number of seconds needed to complete the
reaction and x is the temperature in degrees Celsius at
which the reaction occurs. If the reaction is complete
in 200 seconds, what is the temperature at which the
reaction occurs?
Board
Answer
Solve Quadratic Equations 500
The completion of a certain chemical reaction is
expressed by the equation y = 250 − 5x − x2, where
y is the number of seconds needed to complete the
reaction and x is the temperature in degrees Celsius at
which the reaction occurs. If the reaction is complete
in 200 seconds, what is the temperature at which the
2
y
=
250
–
5x
–
x
reaction occurs?
Where do you put 200 sec?
2
200 = 250 – 5x – x
A 5°C
First, set equal to zero
B 7°C
200 = 250 – 5x – x2
Set each factor = 0
–200 –200
C 10°C
0 = 50 – 5x – x2
x + 10 = 0 and x – 5 = 0
D 12°C
2
+5 +5
–10 –10
Factor x + 5x – 50
Board
( x + 10)( x – 5 ) = 0
x = -10
x =5
Roots 100
The graph of the equation y = x2 – 6x + 8
has which of the following roots?
Board
Answer
Roots 100
The graph of the equation y = x2 – 6x + 8
has which of the following roots?
A
B
C
D
x = –2, x = –4
x = –2, x = 4
x = 2, x = –4
x = 2, x = 4
Board
Roots = Solutions = x-intercepts = Zeros
Algebra
Factor x2 – 6x + 8
( x – 2 )( x – 4 ) = 0
Set each factor = 0
x – 2 = 0 and x – 4 = 0
+2 +2
+4 +4
x=2
x=4
Roots 200
What are the roots of the quadratic equation
x2 − 3x + 2 = 0?
Board
Answer
Roots 200
What are the roots of the quadratic equation
x2 − 3x + 2 = 0?
A
B
C
D
−2 and −1
−2 and 1
2 and −1
2 and 1
Board
Roots = Solutions = x-intercepts = Zeros
Algebra
Factor x2 – 3x + 2
( x – 2 )( x – 1 ) = 0
Set each factor = 0
x – 2 = 0 and x – 1 = 0
+2 +2
+1 +1
x=2
x=1
Roots 300
What are the roots of the function graphed
below?
Board
Answer
Roots 300
What are the roots of the function graphed
below?
F
G
H
J
(−1, −9) and (0, −8)
(0, −4) and (2, 0)
(−4, 0) and (2, 0)
(0, 2) and (0, −4)
Board
Roots 400
What are the x-intercepts of the graph of
the equation y = x2 + x − 12?
Board
Answer
Roots 400
What are the x-intercepts of the graph of
the equation y = x2 + x − 12?
A
B
C
D
x = 4,
x = −4,
x = −4,
x = 4,
Board
x=3
x=3
x = −3
x = −3
Roots = Solutions = x-intercepts = Zeros
Algebra
Factor x2 + x – 12
( x – 3 )( x + 4 ) = 0
Set each factor = 0
x – 3 = 0 and x + 4 = 0
+3 +3
–4 –4
x=3
x = -4
Roots 500
Which ordered pair represents one of the
roots of the function f(x) = 2x2 + 3x − 20?
Board
Answer
Roots 500
Which ordered pair represents one of the
roots of the function f(x) = 2x2 + 3x − 20?
F
5
(− 2 ,
0)
G (−4, 0)
H (−5, 0)
J (−20, 0)
Board
Roots = Solutions = x-intercepts = Zeros
Algebra
Factor 2x2 + 3x – 20
( 2x – 5 )( x + 4 ) = 0
Set each factor = 0
2x – 5 = 0 and x + 4 = 0
+5 +5
–4 –4
2x = 5
x = -4
2
2
5
x
2
Analyze Parabolic2Graphs 100
The graph of the function y = x is given to the
right. How will the graph be affected
if the coefficient of x2 is decreased
to .25 ?
F
G
H
J
The parabola will be
wider.
The parabola will be
narrower.
The parabola will be
translated up.
The parabola will be
translated down.
Board
Answer
Analyze Parabolic2Graphs 100
The graph of the function y = x is given to the
right. How will the graph be affected
if the coefficient of x2 is decreased
to .25 ?
F
G
H
J
The parabola will be
wider.
The parabola will be
narrower.
The parabola will be
translated up.
The parabola will be
translated down.
Board
2
3
Analyze Parabolic Graphs 200
Shirley graphed a function of the form y = ax2 + c. She
then translated the graph 8 units up, resulting in the
function y = − ⅔ x2 + 5. Which of the following best
represents Shirley’s original function?
A
B
C
D
y = - ⅔ x2 + 13
x = - ⅔ x2 + 3
x = - ⅔ x2 - 13
x = - ⅔ x2 - 3
Board
Answer
Analyze Parabolic Graphs 200
Shirley graphed a function of the form y = ax2 + c. She
then translated the graph 8 units up, resulting in the
function y = − ⅔ x2 + 5. Which of the following best
represents Shirley’s original function?
A
B
C
D
y = - ⅔ x2 + 13
x = - ⅔ x2 + 3
x = - ⅔ x2 - 13
x = - ⅔ x2 - 3
Board
Analyze Parabolic Graphs 300
If c = −5, how does the graph of y = x2 + 2c
compare to the graph of y = x2 + c?
F
G
H
.
J
The graph of y = x2 + 2c is below the graph of y = x2 + c.
The graph of y = x2 + 2c is above the graph of y = x2 + c.
The graph of y = x2 + 2c is narrower than the graph of
y = x2 + c.
The graph of y = x2 + 2c is wider than the graph of y = x2 + c.
Board
Answer
Analyze Parabolic Graphs 300
If c = −5, how does the graph of y = x2 + 2c
compare to the graph of y = x2 + c?
F
G
H
.
J
The graph of y = x2 + 2c is below the graph of y = x2 + c.
The graph of y = x2 + 2c is above the graph of y = x2 + c.
The graph of y = x2 + 2c is narrower than the graph of
y = x2 + c.
The graph of y = x2 + 2c is wider than the graph of y = x2 + c.
Board
Analyze Parabolic Graphs 400
The graph of y = 11x2 + c is a parabola with a vertex at the
origin. Which of the following is true about the value of c?
A
B
C
D
c>0
c<0
c=0
c = 11
Board
Answer
Analyze Parabolic Graphs 400
The graph of y = 11x2 + c is a parabola with a vertex at the
origin. Which of the following is true about the value of c?
A
B
C
D
c>0
c<0
c=0
c = 11
Board
Analyze Parabolic Graphs 500
If the graph of y = 19x2 + 31 is translated up 15 units,
which of the following equations will best describe the
resulting graph?
F
G
H
J
y = 34x2 + 31
y = 34x2 + 46
y = 19x2 + 46
y = 19x2 + 16
Board
Answer
Analyze Parabolic Graphs 500
If the graph of y = 19x2 + 31 is translated up 15 units,
which of the following equations will best describe the
resulting graph?
F
G
H
J
y = 34x2 + 31
y = 34x2 + 46
y = 19x2 + 46
y = 19x2 + 16
Board
Problem Solving 100
Mr. Collins invested some money that will
double in value every 12 years. If he invested
$5,000 on the day of his daughter’s birth, how
much will the investment be worth on his
daughter’s 60th birthday?
Board
Answer
Problem Solving 100
Mr. Collins invested some money that will
double in value every 12 years. If he invested
$5,000 on the day of his daughter’s birth, how
much will the investment be worth on his
daughter’s 60th birthday?
A
B
C
D
$300,000
$160,000
$80,000
$320,000
$5,000
Starts at ____________
$10,000
12 years ____________
$20,000
24 years ____________
$40,000
36 years ____________
$80,000
48 years ____________
Board
$160,000
60 years ____________
Problem Solving 200
Herman claimed that the square of a number is always
greater than or equal to the number. Which of the
following examples disproves Herman’s claim?
F A comparison of (−1.5)2 with −1.5
G A comparison of (−0.5)2 with −0.5
H A comparison of (0.5)2 with 0.5
J A comparison of (1.5)2 with 1.5
Board
Answer
Problem Solving 200
Herman claimed that the square of a number is always
greater than or equal to the number. Which of the
following examples disproves Herman’s claim?
F A comparison of (−1.5)2 with −1.5
(−1.5)2 = 2.25
greater than -1.5
2.25 is _______
G A comparison of (−0.5)2 with −0.5
(−0.5)2 = 0.25
greater than -0.5
0.25 is _______
H A comparison of (0.5)2 with 0.5
(0.5)2 = 0.25
less than 0.5
0.25 is _______
J A comparison of (1.5)2 with 1.5
(1.5)2 = 2.25
Board
greater than 1.5
2.25 is _______
Problem Solving 300
The graph of y = 11x2 + c is a parabola with a
vertex at the origin. Which of the following is
true about the value of c?
A
B
C
D
c>0
c<0
c=0
c = 11
Board
Answer
Problem Solving 300
The graph of y = 11x2 + c is a parabola with a
vertex at the origin. Which of the following is
true about the value of c?
A
B
C
D
greater than 0 Like 3, so graph y = 11x2+3
c > 0 Means c is _______
less than 0 Like -3, so graph y = 11x2 –3
c < 0 Means c is _______
equal than 0 So graph y = 11x2 + 0
c = 0 Means c is _______
c = 11
Board
Problem Solving 400
The area of a rectangle is 144j9k15 square units.
If the width of the rectangle is 8j4k5 units, what
is the rectangle’s length?
Board
Answer
Problem Solving 400
The area of a rectangle is 144j9k15 square units.
If the width of the rectangle is 8j4k5 units, what
is the rectangle’s length?
F
G
H
J
1152 j13k20 units
152 j13k20 units
136j5k10 units
18j5k10 units
length times width
Area of a rectangle = ____________________
144j9k15 = Length times 8j4k5
How do you solve? __________
Divide
144 j9 k15
8j4 k 5
144
 18
8
Board
j9
j4
Which means do three problems
 j5
k15
k5
 k10
Problem Solving 500
A science class launches a solar-powered rocket
into the air. The rocket’s height at time t, in
seconds, is expressed by the equation
48 = 2t2 – 4t. How many seconds did it take the
rocket to reach that height?
Board
Answer
Problem Solving 500
A science class launches a solar-powered rocket
into the air. The rocket’s height at time t, in
seconds, is expressed by the equation
48 = 2t2 – 4t. How many seconds did it take the
rocket to reach that height?
A 10
B9
C6
D2
Board
Final Jeopardy Category
Board
Final Jeopardy Question
Which polynomial best represents the area of the
regular hexagon shown below?
[Area =
1
(apothem)(perimeter)]
2
Answer
Final Jeopardy Answer
Which polynomial best represents the area of the
regular hexagon shown below?
1
[Area = 2 (apothem)(perimeter)]
[Area = 0.5(x)(4x + 6)]
[Area =
F
G
H
J
0.5(4x2 + 6x)]
5x + 6
2x2 + 3x
4x2 + 12x
4x + 12
Board
Apothem = x
Perimeter is distance around
12
2
2
2
2
2
2

x6
x 1  x 1 x 1 x 1 x 1 x 1
3
3
3
3
3
3
3