text: CA_GPS_11
  
  # CA_GPS_11 - 1. a) 2 ( ) 4 3 f x x x = ! + b) 5 8 4 ) ( 2 !...
  
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  Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 11 2.1 QUADRATIC FUNCTIONS; PARABOLAS Class Time: ____________ Date: __________ Useful Guidelines: * Quadratic Function: 2 ( ) ,( 0) f x ax bx c a = + + ! , where a , b and c are real numbers. * The vertex of the graph of 2 ( ) ,( 0) f x ax bx c a = + + ! has coordinates ) , ( y x = , 2 2 b b f a a ! " # # ! " \$ % \$ % . * The axis of symmetry of the parabola has equation a b x 2 ! = . * To graph a quadratic function: Step 1: Determine whether the parabola opens up or down. Step 2: Find the vertex. Step 3: Find the x -intercepts (if any) and y -intercept. Step 4: Plot the graph. [Find additional points as needed.] Graph each parabola, Give the vertex, axis, domain, and range.
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  Unformatted text preview: 1. a) 2 ( ) 4 3 f x x x = ! + b) 5 8 4 ) ( 2 ! + ! = x x x f 2. A rocket is fired upward. After t hour, the height of the rocket is given by t t t S 64 2 ) ( 2 + ! = . Find the time required in hours for the rocket to reach maximum height, and find the maximum height in kilometers. 3. The monthly total revenue for a beverage is given by 2 1 . 4000 ) ( x x x R ! = dollars, where x is the number of units sold. a) To maximize the monthly revenue, how many units must be sold? b) What is the maximum possible monthly revenue?...
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  ## This note was uploaded on 10/18/2011 for the course MAC 1105 taught by Professor Russel during the Summer '07 term at Valencia.
  
  Ask a homework question - tutors are online
explanation: The provided text is a college algebra worksheet or study guide that includes several quadratic function problems. It contains a set of instructions and guidelines for graphing quadratic functions, followed by specific problems to solve. The text includes both questions and spaces for answers, but the answers themselves are not filled in. The problems involve graphing parabolas, finding vertices, axes of symmetry, intercepts, and solving real-world applications of quadratic functions.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
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  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: CA_GPS_11
  
  # CA_GPS_11 - 1. a) 2 ( ) 4 3 f x x x = ! + b) 5 8 4 ) ( 2 !...
  
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  Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 11 2.1 QUADRATIC FUNCTIONS; PARABOLAS Class Time: ____________ Date: __________ Useful Guidelines: * Quadratic Function: 2 ( ) ,( 0) f x ax bx c a = + + ! , where a , b and c are real numbers. * The vertex of the graph of 2 ( ) ,( 0) f x ax bx c a = + + ! has coordinates ) , ( y x = , 2 2 b b f a a ! " # # ! " \$ % \$ % . * The axis of symmetry of the parabola has equation a b x 2 ! = . * To graph a quadratic function: Step 1: Determine whether the parabola opens up or down. Step 2: Find the vertex. Step 3: Find the x -intercepts (if any) and y -intercept. Step 4: Plot the graph. [Find additional points as needed.] Graph each parabola, Give the vertex, axis, domain, and range.
  This is the end of the preview. Sign up to access the rest of the document.
  
  Unformatted text preview: 1. a) 2 ( ) 4 3 f x x x = ! + b) 5 8 4 ) ( 2 ! + ! = x x x f 2. A rocket is fired upward. After t hour, the height of the rocket is given by t t t S 64 2 ) ( 2 + ! = . Find the time required in hours for the rocket to reach maximum height, and find the maximum height in kilometers. 3. The monthly total revenue for a beverage is given by 2 1 . 4000 ) ( x x x R ! = dollars, where x is the number of units sold. a) To maximize the monthly revenue, how many units must be sold? b) What is the maximum possible monthly revenue?...
  View Full Document
  
  ## This note was uploaded on 10/18/2011 for the course MAC 1105 taught by Professor Russel during the Summer '07 term at Valencia.
  
  Ask a homework question - tutors are online
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a college algebra worksheet or study guide that includes several quadratic function problems. It contains a set of instructions and guidelines for graphing quadratic functions, followed by specific problems to solve. The text includes both questions and spaces for answers, but the answers themselves are not filled in. The problems involve graphing parabolas, finding vertices, axes of symmetry, intercepts, and solving real-world applications of quadratic functions.
  
  Label: multiple-question