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section31 - k is its y-coordinate Questions 1 When does a...

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MAT 111 - College Algebra Chapter 3 Polynomial Functions A polynomial function is a function of the form f ( x ) = a n x n + a n - 1 x n - 1 + . . . + a 1 x + a 0 where n is a nonnegative integer, a n = 0 and a i R for 0 i n . n is called the degree of the polynomial. Illustrations: 1. f ( x ) = - x 7 + 3 x 2 + 101 x - 1 2. g ( x ) = x 3 + x 2 3. h ( x ) = 1 x 4. k ( x ) = [ | x | ] 5. s ( x ) = | x | Section 3.1 Quadratic Functions Quadratic functions are polynomials of degree 2. The general form of a quadratic function is f ( x ) = a 2 x 2 + a 1 x + a 0 We shall use the letters a , b and c instead of a 2 , a 1 and a 0 . Thus the general form becomes f ( x ) = ax 2 + bx + c Graphs of quadratic functions are always parabolas (a U-shaped graph or a transformation of it).
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In addition to the general or standard form of a parabola, there is another form called the vertex form: f ( x ) = a ( x - h ) 2 + k The above is so called because h is the x -coordinate of the vertex and
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Unformatted text preview: k is its y-coordinate. Questions: 1. When does a parabola open up? When does it open down? f ( x ) = ax 2 + bx + c f ( x ) = a ( x-h ) 2 + k 2. How do we find the coordinates of the vertex of a parabola? f ( x ) = ax 2 + bx + c f ( x ) = a ( x-h ) 2 + k 3. How do we find the equation of axis of symmetry? Examples: 1. Find the quadratic function that has vertex (2,3) and whose graph passes through the point (0,2). 2. Sketch the graph of f ( x ) = 25-x 2 identifying the vertex and intercepts if there are any. 3. Sketch the graph of f ( x ) = x 2 + 3 x + 1 / 4 identifying the vertex and intercepts if there are any....
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