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# 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 could do this with ANY quadratic function to see how the graph relates to our basic squaring function.

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

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