M1410201 - 2.01 CHAPTER 2 POLYNOMIAL AND RATIONAL FUNCTIONS...

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2.01 CHAPTER 2: POLYNOMIAL AND RATIONAL FUNCTIONS SECTION 2.1: QUADRATIC FUNCTIONS (AND PARABOLAS) PART A: BASICS If a , b , and c are real numbers, then the graph of f x ( ) = y = ax 2 + bx + c is a parabola, provided a 0 . If a > 0 , it opens upward . If a < 0 , it opens downward . Examples The graph of y = x 2 4 x + 5 (with a = 1 > 0 ) is on the left. The graph of y = x 2 + 4 x 3 (with a = 1 < 0 ) is on the right.
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2.02 PART B: FINDING THE VERTEX AND THE AXIS OF SYMMETRY (METHOD 1) The vertex of the parabola [with equation] y = ax 2 + bx + c is h , k ( ) , where: x -coordinate = h = b 2 a , and y -coordinate = k = f h ( ) . The axis of symmetry, which is the vertical line containing the vertex, has equation x = h . (Does the formula for h look familiar? We will discuss this later.) Example Find the vertex of the parabola y = x 2 6 x + 5 . What is its axis of symmetry? Solution The vertex is h , k ( ) , where: h = b 2 a = 6 2 1 ( ) = 3 , and k = f 3 ( ) = 3 ( ) 2 6 3 ( ) + 5 = 4 The vertex is 3, 4 ( ) . The axis of symmetry has equation x = 3 . Since a = 1 > 0 , we know the parabola opens upward . Together with the vertex, we can do a basic sketch of the parabola.
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2.03 PART C: FINDING MORE POINTS “Same” Example: y = x 2 6 x + 5 , or f x ( ) = x 2 6 x + 5 Find the y -intercept. Plug in 0 for
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M1410201 - 2.01 CHAPTER 2 POLYNOMIAL AND RATIONAL FUNCTIONS...

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