Section 8.1

# Section 8.1 - Section 8.1 Quadratic Functions and Their...

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Section 8.1 Quadratic Functions and Their Graphs 1

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Quadratic Function A quadratic function can be written in the form Where a , b , and c are constants with a 0 2 ( ) , f x ax bx c = + + 2
Graphing f(x) = x 2 2 2 2 2 2 What happens to when we do these things? 2 1 2 When 1, the graph is vertically stretched (made narrower). When 0 1, the graph is compressed (made wider). When 0, the par y x y x y x y ax y x a a a = = = = = - < < abola opens up (has a minimum value). When 0, the parabola opens down (has a maximum value). a < 3

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Identify the vertex, axis of symmetry, and whether the parabola opens upward or downward. Does the graph have a minimum or a maximum? State where the graph is increasing and where it is decreasing. a) b) -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y 4
The Vertex of a Parabola 2 The vertex of the parabola given by ( ) is , 2 2 The x-coordinate of the vertex is - . 2

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Section 8.1 - Section 8.1 Quadratic Functions and Their...

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