Mth141S32n - Sec. 3.2 Quadratic Functions, and Graphs A...

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Sec. 3.2 – Quadratic Functions, and Graphs A quadratic function is a polynomial function of degree two. Therefore, there will be an 2 x term. The graph of a quadratic function can be found from the squaring function, i.e. 2 ( ) f x x = . It will be a parabola! Given a quadratic function in its normal polynomial form, we can change it to one with reflections, shifts and/or stretches/contractions. For ex. if 2 ( ) 2 2 3 f x x x = + + then we can use the complete the square process ! 2 ( ) 3 2 2 f x x x = + + divide both sides by 2 2 ( ) 3 ____ 2 2 f x x x - = + + subtract 3/2 from both sides 2 ( ) 3 1 1 2 2 4 4 f x x x - + = + + add ¼ to both sides 2 ( ) 5 1 2 4 2 f x x - = + simplify and factor 2 ( ) 1 5 2 2 4 f x x = + + add 5/4 to both sides, now multiply thru by 2 2 1 1 ( ) 2( ) 2 2 2 f x x = + + so we stretch the 2 x graph by 2 vertically, shift it 1 2 a unit to the left, and up 1 2 2 . Notice that the “origin” point of 2 x , shifts to 1 1 ( ,2 ) 2 2 - . This is the low point of the graph and is called the vertex of the parabola! It is the high/low point of the parabola, depending upon which way the parabola opens. We
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This note was uploaded on 06/06/2011 for the course MTH mth141 taught by Professor Stean during the Spring '10 term at Moraine Valley Community College.

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Mth141S32n - Sec. 3.2 Quadratic Functions, and Graphs A...

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