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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

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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

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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