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Let’s Get Ready. To Play Some. J. E. O. P. A. R. D. Y. J E O P A R D Y. J E O P A R D Y. J E O P A R D Y. J E O P A R D Y. J E O P A R D Y. Jeopardy Board. Final Jeopardy. Solve Quadratic Equations 100. What is the solution set for the equation 3x 2 – 4x +1 = 0?. Board. - PowerPoint PPT Presentation
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Let’s Get ReadyLet’s Get ReadyTo Play Some . . .
JJEOPARDYJEOPARDYJEOPARDYJEOPARDYJEOPARDYJEOPARDYJEOPARDYJEOPARDYJEOPARDYJEOPARDYJEOPARDY
Solve Quadratic Equations Roots
Analyze Parabolic Graphs
Problem Solving
100 100 100 100
200 200 200 200
300 300 300 300
400 400 400 400
500 500 500 500
Final Jeopardy
Jeopardy BoardJeopardy Board
Board Answer
Solve Quadratic Equations 100What is the solution set for the equation 3x2 – 4x +1 = 0?
Board
Solve Quadratic Equations 100
1A 1,
3
11 11B ,
6 6
8 8C ,
6 6
1D 1,
3
What is the solution set for the equation 3x2 – 4x +1 = 0?
AlgebraFactor 3x2 – 4x + 1( )( ) = 03x x– 1 – 1
Set each factor = 0
3x – 1 = 0 and x – 1 = 0+1 +1 3x = 13 3
1x
3
+1 +1
x = 1
Graphing
Board Answer
Solve Quadratic Equations 200The polynomial x2 + x − 6 is modeled below using algebraic tiles.
What are the solutions to the equation x2 + x = 6?
A x = −3 and x = −2B x = −3 and x = 2C x = 3 and x = −2D x = 3 and x = 2
Board
Solve Quadratic Equations 200The polynomial x2 + x − 6 is modeled below using algebraic tiles.
What are the solutions to the equation x2 + x = 6?
Factor x2 + x – 6
( )( ) = 0x x+ 3 – 2
Set each factor = 0
x + 3 = 0 and x – 2 = 0–3 –3 x = -3
+2 +2 x = 2
First, set equal to zerox2 + x = 6
–6 –6 x2 + x – 6 = 0
Board Answer
Solve Quadratic Equations 300What is the solution set for the equation 4(3x − 2)2 = 36
A {− , }
B {− , }
C {− , }
D {− , }
11
611
31
3
5
32
3
4
3
11
611
3
Board
Solve Quadratic Equations 300What is the solution set for the equation 4(3x − 2)2 = 36 First, set equal to zero
4(3x − 2)2 = 36 –36 –36
4(3x − 2)2 – 36 = 0
ENTER
ENTERENTER
2nd QUIT 2nd ANS (-)
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
F Between 0 and 0.5 sec.G Between 1 and 1.5 sec.H Between 0.5 and 1 sec. and 1.5 and 2 sec.J Between 1 and 1.5 sec. and 1.5 and 2 sec.
Board
Solve Quadratic Equations 400Nancy 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
Path of the ball Height of 70 It occurs twice
Board Answer
Solve Quadratic Equations 500The 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
Solve Quadratic Equations 500
A 5°CB 7°CC 10°CD 12°C
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? y = 250 – 5x – x2
Where do you put 200 sec?200 = 250 – 5x – x2
Factor x2 + 5x – 50
( )( ) = 0x x+ 10 – 5
Set each factor = 0
x + 10 = 0 and x – 5 = 0–10 –10 x = -10
+5 +5 x = 5
First, set equal to zero200 = 250 – 5x – x2
–200 –200 0 = 50 – 5x – x2
Board Answer
Roots 100The graph of the equation y = x2 – 6x + 8 has which of the following roots?
A x = –2, x = –4B x = –2, x = 4C x = 2, x = –4D x = 2, x = 4
Board
Roots 100The graph of the equation y = x2 – 6x + 8 has which of the following roots?
Roots = Solutions = x-intercepts = ZerosAlgebraFactor x2 – 6x + 8( )( ) = 0x x– 2 – 4
Set each factor = 0
x – 2 = 0 and x – 4 = 0+2 +2 x = 2
+4 +4 x = 4
Board Answer
Roots 200What are the roots of the quadratic equation x2 − 3x + 2 = 0?
A −2 and −1B −2 and 1C 2 and −1D 2 and 1
Board
Roots 200What are the roots of the quadratic equation x2 − 3x + 2 = 0?
Roots = Solutions = x-intercepts = ZerosAlgebraFactor x2 – 3x + 2
( )( ) = 0x x– 2 – 1
Set each factor = 0
x – 2 = 0 and x – 1 = 0+2 +2 x = 2
+1 +1 x = 1
Board Answer
Roots 300What are the roots of the function graphed below?
F (−1, −9) and (0, −8)G (0, −4) and (2, 0)H (−4, 0) and (2, 0)J (0, 2) and (0, −4)
Board
Roots 300What are the roots of the function graphed below?
Board Answer
Roots 400
What are the x-intercepts of the graph of the equation y = x2 + x − 12?
A x = 4, x = 3B x = −4, x = 3C x = −4, x = −3D x = 4, x = −3
Board
Roots 400What are the x-intercepts of the graph of the equation y = x2 + x − 12?
Roots = Solutions = x-intercepts = ZerosAlgebraFactor x2 + x – 12 ( )( ) = 0x x– 3 + 4
Set each factor = 0
x – 3 = 0 and x + 4 = 0+3 +3 x = 3
–4 –4x = -4
Board Answer
Roots 500Which ordered pair represents one of the roots of the function f(x) = 2x2 + 3x − 20?
F (− , 0)
G (−4, 0)
H (−5, 0)
J (−20, 0)
5
2
Board
Roots 500Which ordered pair represents one of the roots of the function f(x) = 2x2 + 3x − 20?
Roots = Solutions = x-intercepts = ZerosAlgebraFactor 2x2 + 3x – 20
( )( ) = 02x x– 5 + 4
Set each factor = 0
2x – 5 = 0 and x + 4 = 0+5 +5 2x = 5
– 4 – 4 x = -4
2 2 5
x2
Board Answer
Analyze Parabolic Graphs 100
Board
Analyze Parabolic Graphs 100
Board Answer
Analyze Parabolic Graphs 200
Board
Analyze Parabolic Graphs 200
Board Answer
Analyze Parabolic Graphs 300
Board
Analyze Parabolic Graphs 300
Board Answer
Analyze Parabolic Graphs 400
Board
Analyze Parabolic Graphs 400
Board Answer
Analyze Parabolic Graphs 500
Board
Analyze Parabolic Graphs 500
Board Answer
Problem Solving 100Mr. 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 $300,000B $160,000C $80,000D $320,000
Board
Problem Solving 100Mr. 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?
Starts at ____________$5,000
12 years ____________$10,000
24 years ____________$20,000
36 years ____________$40,000
48 years ____________$80,000
60 years ____________$160,000
Board Answer
Problem Solving 200Herman 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
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
Problem Solving 200
(−1.5)2 = 2.25 2.25 is _______ than -1.5greater
(−0.5)2 = 0.25 0.25 is _______ than -0.5greater
(0.5)2 = 0.25 0.25 is _______ than 0.5less
(1.5)2 = 2.25 2.25 is _______ than 1.5greater
Board Answer
Problem Solving 300The 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 c > 0B c < 0C c = 0D c = 11
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 c > 0B c < 0C c = 0D c = 11
Board
Problem Solving 300
Means c is _______ than 0greater Like 3, so graph y = 11x2+3
Means c is _______ than 0less Like -3, so graph y = 11x2 –3
Means c is _______ than 0equal So graph y = 11x2 + 0
Board Answer
Problem Solving 400The area of a rectangle is 144j9k15 square units. If the width of the rectangle is 8j4k5 units, what is the rectangle’s length?
F 1152 j13k20 unitsG 152 j13k20 unitsH 136j5k10 unitsJ 18j5k10 units
Board
Problem Solving 400The area of a rectangle is 144j9k15 square units. If the width of the rectangle is 8j4k5 units, what is the rectangle’s length?
Area of a rectangle = ____________________length times width
144j9k15 = Length times 8j4k5
How do you solve? __________Divide9 15
4 5
144j k
8j kWhich means do three problems
144
8 18
9
4
j
j j5
15
5
k
kk10
Board Answer
Problem Solving 500A 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 10B 9C 6D 2
Board
Problem Solving 500A 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?
Final Jeopardy Category
Final Jeopardy Category
Board
[Area = (apothem)(perimeter)]
Final Jeopardy QuestionFinal Jeopardy Question
Answer
1
2
Which polynomial best represents the area of the regular hexagon shown below?
Board
Final Jeopardy AnswerFinal Jeopardy Answer
[Area = (apothem)(perimeter)]
Which polynomial best represents the area of the regular hexagon shown below?
F 5x + 6G 2x2 + 3xH 4x2 + 12xJ 4x + 12
[Area = 0.5(x)(4x + 6)]
Apothem = x
Perimeter is distance around2
x 13
2
x 13
2
x 13
2
x 13
2
x 13
2
x 13
12
x 63
[Area = 0.5(4x2 + 6x)]
1
2