mac1147_lecture11_1_b

mac1147_lecture11_1_b - L11 Quadratic Functions and Models;...

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132 L11 Quadratic Functions and Models; Polynomial Functions and Inequalities Quadratic Function The quadratic function is a function of the form 2 () f x ax bx c = ++ where a, b, and c are real numbers and 0 a . Example . Use the graph of 2 fx x = as a reference to sketch the graphs of the following functions: 2 2 hx x =− 2 1 2 mx x = 22 8 1 7 ( 4 ) 1 gx x x x =−+=− +
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133 By completing the square, the equation of a quadratic function 2 () f x ax bx c =+ + , 0 a , can be written in the form 2 ( ) fx ax h k = −+ , where 2 b h a = and 2 4 4 ac b k a = or ( ) kf h = . The Graph of 2 f x ax bx c = ++ ( 0 a ) is _________ Vertex : Axis : Parabola opens up if _______; ( ) fh k = is the minimum value of f . Parabola opens down if _______; k = is the maximum value of f . Compared with the graph of 2 fx x = , the graph of 2 fx a x b x c + is: stretched vertically if 1 a > ; compressed vertically if 01 a < < .
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134 Example : Find the vertex, axis, intercepts, domain, and range. Graph the parabola. 2 () 2 1 2 1 0 fx x x =++
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135 Applications of the Quadratic Function Example : Suppose that a baseball is tossed straight up, and its height s (in feet) as a function of time t (in seconds) is given by 2 ( ) 16 64 6 s tt t = −+ + , with 0 t = corresponding to the instant when the ball is released. When does the ball reach the maximum height? What is the maximum height of the ball?
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136 Economics: Demand Equations The price p and the quantity x sold of a certain product obey the demand equation 1 18, 0 90 5 px x =− + ≤ ≤ (a) Express the revenue R as a function of x. (b) What is the revenue if 80 units are sold? (c) What quantity x maximizes revenue? What is the maximum revenue?
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mac1147_lecture11_1_b - L11 Quadratic Functions and Models;...

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