Factoring Word Problems Properties Vertex Square Roots 100
Factoring Word Problems Properties Vertex Square Roots 100 100 100 200 200 200 300 300 300 400 400 400 500 500 500 Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team 7 Team 8
What does the “c” tell you in a quadratic function? Properties 100
Answer: the y-intercept of the graph
Given this equation, Determine the solutions using factoring. Properties 200
Answer: x = -4 x = -1
Create a quadratic equation that opens up with a y-intercept below the origin. Properties 300
Answer: answers vary… must have +a and a -c
Determine the AOS and Vertex of the given quadratic function. Describe how the graph would look. Properties 400
Answer: AOS x = 2 Vertex (2, 8) Graph opens up has a y-intercept at (0, 10) and is relatively fat.
Create a quadratic equation that has a maximum, is relatively skinny, has a vertex not on the y-axis, and has a y -intercept above zero. Properties 500
Answer: answers vary must have “–a” that’s relatively big, must have a “b” value and a “–c” value.
What is the vertex? Vertex 100
Answer: (0, -5)
What is the vertex? Vertex 200
Answer: (4, 1)
State the steps to determine the vertex. Vertex 300
Answer: to find the vertex; first find the AOS x=-b/2 a, then plug the x in to find y. The vertex is the resulting ordered pair.
Explain how it is possible that the vertex and the y-intercept are the same. Vertex 400
Answer: the vertex and yintercept are the same if there is a quadratic function with no “b” value because then your AOS is x=0 which is the y-axis
State the AOS and vertex. Vertex 500
Answer: x =. 25 (. 25, 3. 5)
Solve the quadratic equation: Square Roots 100
Answer: x=14
Solve the quadratic equation: Square Roots 200
Answer: no solution
Solve the quadratic equation: Square Roots 300
Answer: x=8
The formula for the volume of a cylinder is Determine the radius of a cylinder if the height is 6 inches and the volume is approximately 381. 7 inches. Square Roots 400
Answer: radius is approximately 4. 5 inches
The height h(t) of a coin dropped off the Leaning Tower of Pisa in Italy is a function of time t in seconds. Hamad drops a coin. How long does it take the coin to be at a height of 100 ft? Round to hundredths Square Roots 500
Answer: approximately 2. 29 seconds
Factor the expression Factoring 100
Answer: (x + 1)(x – 2)
Factor the expression Factoring 200
Answer:
Factor the expression Factoring 300
Answer: (4 x+3)(2 x+1)
Factor the expression Factoring 400
Answer: (3 x-9)(3 x+9)
Tell whether each polynomial can be factored. Justify your answer. Factoring 500
Answer: the first one can because 5*2 =10 and 5+2 =7 but the second one can’t be factored because nothing multiplies to 5 and adds to -4.
A Danish tire manufacturer finds that the cost (C ) in Kroner of manufacturing tires is a function of the number (n ) of tires that they produce modeled by the equation Find the number of tires that minimizes the cost of production. Word Problems 100
Answer: 2000 tires
You toss a ball to a friend who is on a balcony. Your friend catches the ball at its highest point. At what height does she catch it (ft)? Word Problems 200
Answer: 25. 78125 ft
A model rocket is launched off the top of a platform. The height of the rocket is given by the function h(t)= -4. 9 t 2 + 86 t + 2. 1, where h(t) is the height in meters and t is the time in seconds. Round to the nearest tenth if necessary. A) When will the rocket reach its highest point? B) B) How high will the rocket be at its highest point? Word Problems 300
Answer: A) 8. 8 seconds B) 379. 4 meters
Your friend drops a ball from the top of a 10 foot tree. Suppose the situation is modeled by the equation According to this model, when will the ball hit the ground? Word Problems 400
Answer: seconds
When a football player punts a football, he hopes for a long “hang time. ” Manel is the punter for his middle school team. He can kick the ball with an upward velocity of 80 ft/s and his foot meets the ball 2 feet off the ground. Write a quadratic function to describe the height of the ball at any given time. Use 32 ft/s as the acceleration of gravity. Word Problems 500
Answer:
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