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1140 L13 - Lecture 13 Section 2.1 Quadratic Functions and...

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Lecture 13: Section 2.1 Quadratic Functions and Models Def. A quadratic function is a second degree polynomial of the form f ( x ) = ax 2 + bx + c where a; b and c are real numbers and a 6 = 0. NOTE: The graph of a quadratic function is a transformation of the parent function f ( x ) = x 2 . Its graph is in the shape of ’U’ called a parabola . ex. Graph f ( x ) = ( x 3) 2 + 2
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Standard form of a quadratic function The quadratic function can be written in standard form f ( x ) = a ( x h ) 2 + k; a 6 = 0 The standard form is convenient for sketching: 1. Vertex: 2. Axis of Symmetry: All parabolas are symmetric with respect to a line called axis of symmetry . 3. Parabola opens upward if ; The vertex ( h; k ) is the point. Parabola opens downward if ; The vertex ( h; k ) is the point. 4. The graph is a transformation of f ( x ) = x 2 . If j a j > 1, the graph is stretched vertically and if 0 < j a j < 1, the graph is compressed vertically .
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To write a quadratic function in standard form, we complete the square .
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