Obj18to24Sp11

Obj18to24Sp11 - Objective 18 Quadratic Functions The...

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Objective 18 Quadratic Functions The simplest quadratic function is f ( x )= x 2 . x y Objective 18b Quadratic Functions in ( h, k ) form Applying all of Obj 14 (re±ections and translations) to the function. f ( x a ( x - h ) 2 + k vertex a> 0 parabola opens a< 0 parabola opens Objective 18a Quadratic Functions in Standard form f ( x ax 2 + bx + c What’s the vertex? We could and put it in ( h, k ) form. Good news: f ( x ax 2 + bx + c vertex 0 parabola opens 0 parabola opens For either quadratic form: To ²nd x -intercepts, let solve for x . To ²nd y -intercepts, let solve for y . Sometimes we ask “How many x -intercepts are there?” For Obj 18a, You can use the For Obj 18b, Just 1
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Objective 18c Max/Min of Quadratic Function x y x y Ob 18a example The information included in this example would be asked in separate eGrade problems. f ( x )= - 12 x 2 - 4 x +1 Opens Up/Down x -coordinate of vertex = How many x -intercepts? Max/Min is Max/Min is at x = Find all intercepts. (For eGrade problem: Enter them in any order separated by semicolon.) Which of the following most closely resembles the graph of f ( x - 12 x 2 - 4 x + c ? y x x y x y x y 2
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Ob 18b example The information included in this example would be asked in separate eGrade problems. f ( x )= a ( x + 1) 2 - 8 , a > 0 Opens Up/Down vertex = How many x -intercepts? Max/Min is Max/Min is at x = Find all intercepts for f ( x ) = 2( x +1) 2 - 8. (For eGrade problem: Enter them in any order separated by semicolon.) Find all intercepts for f ( x ) = 2(2 x + 1) 2 - 10. (For eGrade problem: Enter them in any order separated by semicolon.) Which of the following most closely resembles the graph of f ( x a ( x + 1) 2 - 2 , a > 0? y x x y x y x y 3
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Ob 18c example Studies have found that the relationship between advertising dollars, a , in thou- sands, and revenue, R , can be modeled by a quadratic function. If R ( a )= - 4 a 2 +364 a +2569 . 5, how many thousands of advertising dollars should be spent in order to maximize revenue? (Enter number answer - integers or exact decimals; mathematical operators are not allowed. For example, 15 / 2 must be entered as 7 . 5. Don’t type any dollar signs, commas, or units. The function given does not represent the results of an actual study.) Ob 18c example A large swimming pool is treated regularly to control the growth of harmful bacteria. If the concentration of bacteria, C (per cubic centimeter), t days after treatment, is given by C ( t ) = 0 . 4 t 2 - 4 . 4 t + 30 . 1, What is the minimum concentration of bacteria? (Same eGrade cautions as in previous example.) 4
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Objective 19 Power Functions f ( x )= x n , where n is an integer, n 2 The power functions are classi±ed into 2 groups: f ( x x n , where n is an even positive integer, n 2 For example: f ( x x 2 , f ( x x 4 , f ( x x 6 , ... f ( x x 58 , ...
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Obj18to24Sp11 - Objective 18 Quadratic Functions The...

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