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Solve Quadratic Equations Roots Analyze Parabolic Graphs Problem Solving Final Jeopardy Jeopardy Board

BoardAnswer Solve Quadratic Equations 100 What is the solution set for the equation 3x 2 – 4x +1 = 0?

Board Solve Quadratic Equations 100 What is the solution set for the equation 3x 2 – 4x +1 = 0? Algebra Factor 3x 2 – 4x + 1 ( )( ) = 03xx– 1 Set each factor = 0 3x – 1 = 0 and x – 1 = x = x = 1 Graphing

BoardAnswer Solve Quadratic Equations 200 The polynomial x 2 + x − 6 is modeled below using algebraic tiles. What are the solutions to the equation x 2 + x = 6?

A x = −3 and x = −2 B x = −3 and x = 2 C x = 3 and x = −2 D x = 3 and x = 2 Board Solve Quadratic Equations 200 The polynomial x 2 + x − 6 is modeled below using algebraic tiles. What are the solutions to the equation x 2 + x = 6? Factor x 2 + x – 6 ( )( ) = 0 xx+ 3– 2 Set each factor = 0 x + 3 = 0 and x – 2 = 0 –3 x = x = 2 First, set equal to zero x 2 + x = 6 –6 x 2 + x – 6 = 0

BoardAnswer Solve Quadratic Equations 300 What is the solution set for the equation 4(3x − 2) 2 = 36

A {−, } B {−, } C{−, } D {−, } Board Solve Quadratic Equations 300 What is the solution set for the equation 4(3x − 2) 2 = 36 First, set equal to zero 4(3x − 2) 2 = 36 –36 4(3x − 2) 2 – 36 = 0 ENTER 2 nd QUIT 2 nd 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 BoardAnswer Solve Quadratic Equations 400

F Between 0 and 0.5 sec. G Between 1 and 1.5 sec. HBetween 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 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 Path of the ballHeight of 70It occurs twice

BoardAnswer Solve Quadratic Equations 500 The completion of a certain chemical reaction is expressed by the equation y = 250 − 5x − x 2, 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 A5°C B 7°C C 10°C D 12°C The completion of a certain chemical reaction is expressed by the equation y = 250 − 5x − x 2, 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 – x 2 Where do you put 200 sec? 200 = 250 – 5x – x 2 Factor x 2 + 5x – 50 ( )( ) = 0 xx+ 10– 5 Set each factor = 0 x + 10 = 0 and x – 5 = 0 –10 x = x = 5 First, set equal to zero 200 = 250 – 5x – x 2 –200 0 = 50 – 5x – x 2

BoardAnswer Roots 100 The graph of the equation y = x 2 – 6x + 8 has which of the following roots?

A x = –2, x = –4 B x = –2, x = 4 C x = 2, x = –4 D x = 2, x = 4 Board Roots 100 The graph of the equation y = x 2 – 6x + 8 has which of the following roots? Roots = Solutions = x-intercepts = Zeros Algebra Factor x 2 – 6x + 8 ( )( ) = 0xx– 2– 4 Set each factor = 0 x – 2 = 0 and x – 4 = 0 +2 x = 2 +4 x = 4

BoardAnswer Roots 200 What are the roots of the quadratic equation x 2 − 3x + 2 = 0?

A −2 and −1 B −2 and 1 C 2 and −1 D 2 and 1 Board Roots 200 What are the roots of the quadratic equation x 2 − 3x + 2 = 0? Roots = Solutions = x-intercepts = Zeros Algebra Factor x 2 – 3x + 2 ( )( ) = 0xx– 2– 1 Set each factor = 0 x – 2 = 0 and x – 1 = 0 +2 x = 2 +1 x = 1

BoardAnswer Roots 300 What 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 300 What are the roots of the function graphed below?

BoardAnswer Roots 400 What are the x-intercepts of the graph of the equation y = x 2 + x − 12?

A x = 4, x = 3 Bx = −4, x = 3 C x = −4, x = −3 D x = 4, x = −3 Board Roots 400 What are the x-intercepts of the graph of the equation y = x 2 + x − 12? Roots = Solutions = x-intercepts = Zeros Algebra Factor x 2 + x – 12 ( )( ) = 0xx– 3+ 4 Set each factor = 0 x – 3 = 0 and x + 4 = 0 +3 x = 3 –4 x = -4

BoardAnswer Roots 500 Which ordered pair represents one of the roots of the function f(x) = 2x 2 + 3x − 20?

F (−, 0) G(−4, 0) H (−5, 0) J (−20, 0) Board Roots 500 Which ordered pair represents one of the roots of the function f(x) = 2x 2 + 3x − 20? Roots = Solutions = x-intercepts = Zeros Algebra Factor 2x 2 + 3x – 20 ( )( ) = 02xx– 5+ 4 Set each factor = 0 2x – 5 = 0 and x + 4 = x = 5 – 4 x =

BoardAnswer Analyze Parabolic Graphs 100

Board Analyze Parabolic Graphs 100

BoardAnswer Analyze Parabolic Graphs 200

Board Analyze Parabolic Graphs 200

BoardAnswer Analyze Parabolic Graphs 300

Board Analyze Parabolic Graphs 300

BoardAnswer Analyze Parabolic Graphs 400

Board Analyze Parabolic Graphs 400

BoardAnswer Analyze Parabolic Graphs 500

Board Analyze Parabolic Graphs 500

BoardAnswer 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 $300,000 B$160,000 C $80,000 D $320,000 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? Starts at ____________ $5, years ____________ $10, years ____________ $20, years ____________ $40, years ____________ $80, years ____________ $160,000

BoardAnswer 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 HA 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 HA 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 = is _______ than -1.5 greater (−0.5) 2 = is _______ than -0.5 greater (0.5) 2 = is _______ than 0.5 less (1.5) 2 = is _______ than 1.5 greater

BoardAnswer Problem Solving 300 The graph of y = 11x 2 + c is a parabola with a vertex at the origin. Which of the following is true about the value of c? A c > 0 B c < 0 Cc = 0 D c = 11

The graph of y = 11x 2 + c is a parabola with a vertex at the origin. Which of the following is true about the value of c? A c > 0 B c < 0 Cc = 0 D c = 11 Board Problem Solving 300 Means c is _______ than 0 greater Like 3, so graph y = 11x 2 +3 Means c is _______ than 0 less Like -3, so graph y = 11x 2 –3 Means c is _______ than 0 equal So graph y = 11x 2 + 0

BoardAnswer Problem Solving 400 The area of a rectangle is 144j 9 k 15 square units. If the width of the rectangle is 8j 4 k 5 units, what is the rectangle’s length?

F 1152 j 13 k 20 units G 152 j 13 k 20 units H 136j 5 k 10 units J18j 5 k 10 units Board Problem Solving 400 The area of a rectangle is 144j 9 k 15 square units. If the width of the rectangle is 8j 4 k 5 units, what is the rectangle’s length? Area of a rectangle = ____________________ length times width 144j 9 k 15 = Length times 8j 4 k 5 How do you solve? __________Divide Which means do three problems 18j5j5 k 10

BoardAnswer 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 = 2t 2 – 4t. How many seconds did it take the rocket to reach that height?

A 10 B 9 C 6 D 2 Board 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 = 2t 2 – 4t. How many seconds did it take the rocket to reach that height?

Final Jeopardy Category Board

[Area = (apothem)(perimeter)] Final Jeopardy Question Answer Which polynomial best represents the area of the regular hexagon shown below?

Board Final Jeopardy Answer [Area = (apothem)(perimeter)] Which polynomial best represents the area of the regular hexagon shown below? F 5x + 6 G 2x 2 + 3x H 4x x J 4x + 12 [Area = 0.5(x)(4x + 6)] Apothem = x Perimeter is distance around [Area = 0.5(4x 2 + 6x)]