1-4 - 1-4 Quadratic Functions and Their Graphs Quadratic...

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1-4 Quadratic Functions and Their Graphs Quadratic function: has a squared term, but none of higher degree standard form of the quadratic function : f(x) = ax 2 + bx + c (a 0) vertex = b 2a f b 2a , vertex form of the quadratic function: f(x) = a(x - h) 2 + k vertex = (h, k) parabola : the graph of a quadratic function The anatomy of a parabola The role of a : if a > 0, parabola opens upward if a < 0, parabola opens downward 1-4 p. 1
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Finding the vertex Example: f(x) = (x + 1) 2 - 3 It is already in vertex form f(x)= (x - h) 2 + k so vertex = (h, k) = (-1, -3) Example: f(x) = x 2 + 2x - 2 x-coordinate of vertex = -b/2a = -2/2 = -1 y-coordinate of vertex = f( -1 ) = (-1) 2 + 2(-1) –2 = -3 so vertex = (-1, -3) Note: this is not the way shown in the book (i.e. by completing the square), but is far superior to it 1-4 p. 2
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Sketching the graph of a quadratic function Example: R(x) = x(2000 – 60x) 1 ≤ x ≤ 25 (1) write it in standard form: R(x) = 2000x – 60x 2 (2) find the vertex: x-coordinate = -b/2a = -2000/-120 = 50/3 = 16.67 y-coordinate = 50/3(2000 – 60(50/3)) = 16667 (3)
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