mac1140_lecture19_1

# mac1140_lecture19_1 - L19 4.1 Quadratic Functions A...

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162 L19 §4.1 Quadratic Functions A function f is called a quadratic function if 2 () f x ax bx c = ++ , where a , b , and c are real numbers and 0 a . Example . Sketch the graph of the function 2 ( 2 ) 3 gx x =− + +

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163 Example . Sketch the graph of the function 2 1 2 () ( 3 ) 2 fx x =− + Ve r tex : In general : The graph of a quadratic function 2 ( ) fx ax h k = −+ is a parabola with vertex ( , ) hk and axis x h = . It opens upward if ______ & downward if_______ 1 a >⇒ 01 a <<
164 Starting with the general equation of a quadratic function 2 () f x ax bx c = ++ , we can reduce it to the form 2 ( ) fx ax h k = −+ by completing the square, which allows as to obtain the general formula for the vertex of the parabola (,) hk . 2 f x ax bx c =+ + 2 2 24 bb fx ax c aa ⎛⎞ + ⎜⎟ ⎝⎠ Compare with 2 ( ) k =− + . Important Result: h = k = Important Note: kf h =

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165 Example . Given 2 () 3 1 2 7 fx x x = −+ . Find the vertex and sketch the graph.
166 Example . Sketch the graph of 2 () 2 5 hx x x = −− . Find the vertex and all intercepts.

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167 Example : Suppose that a baseball is tossed straight up,
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mac1140_lecture19_1 - L19 4.1 Quadratic Functions A...

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