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Chapter 8 Notes.pptx

Chapter 8 Notes.pptx - 8.4 The Quadratic Formula 8.3...

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8.2 Parabolas and Modeling 8.1 Quadratic Functions and Their Graphs Chapter 8 – Quadratic Functions and Equations 8.4 The Quadratic Formula 8.3 Quadratic Equations
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8.2 Parabolas and Modeling 8.1 Quadratic Functions and Their Graphs Chapter 8 – Quadratic Functions and Equations 8.4 The Quadratic Formula 8.3 Quadratic Equations
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8.1 Quadratic Functions and Their Graphs The graph of any quadratic function is a parabola . The vertex is the lowest point on the graph of a parabola that opens upward and the highest point on the graph of a parabola that opens downward.
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8.1 Quadratic Functions and Their Graphs The graph is symmetric with respect to the y -axis. In this case the y -axis is the axis of symmetry for the graph.
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8.1 Quadratic Functions and Their Graphs Use the graph of the quadratic function to identify the vertex, axis of symmetry, and whether the parabola opens upward or downward. a. b. Vertex (0, 2) Axis of symmetry: x = –2 Open: up Vertex (0, 4) Axis of symmetry: x = 0 Open: down
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8.1 Quadratic Functions and Their Graphs Find the vertex for the graph of a = 2 and b = 8 Substitute into the equation to find the y -value. The vertex is ( 2, 11), which is supported by the graph. 2 ( ) 2 8 3. f x x x 8 2 2(2) x     2 b x a   2 ( ) 2( 2) 8( 2) 3 8 16 3 11 f x  
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8.1 Quadratic Functions and Their Graphs Identify the vertex, and the axis of symmetry on the graph, then graph. Solution Begin by making a table of values. Plot the points and sketch a smooth curve. The vertex is (0, –2) axis of symmetry x = 0 x f ( x ) = x 2 – 2 3 7 2 2 1 1 0 2 1 1 2 2 3 7 2 ( ) 2 f x x
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8.1 Quadratic Functions and Their Graphs Identify the vertex, and the axis of symmetry on the graph, then graph. Solution Begin by making a table of values. Plot the points and sketch a smooth curve. The vertex is (2, 0) axis of symmetry x = 2 x g ( x ) = ( x – 2) 2 0 4 1 1 2 0 3 1 4 4 2 ( ) ( 2) g x x  
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8.1 Quadratic Functions and Their Graphs Identify the vertex, and the axis of symmetry on the graph, then graph. Solution Begin by making a table of values. Plot the points and sketch a smooth curve. The vertex is (2, 0) Axis of symmetry x = 2 x h ( x ) = x 2 – 2 x – 3 2 5 1 0 0 3 1 4 2 3 3 0 4 5 2 ( ) 2 3 h x x x
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8.1 Quadratic Functions and Their Graphs Find the maximum y -value of the graph of Solution The graph is a parabola that opens downward because a < 0. The highest point on the graph is the vertex. a = 1 and b = 2 2 ( ) 2 3. f x x x   ( 2) 1 2 2( 1) b x a       2 ( ) ( 1) 2( 1) 3 4 f x   
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8.1 Quadratic Functions and Their Graphs A baseball is hit into the air and its height h in feet after t seconds can be calculated by a. What is the height of the baseball when it is hit?
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