Section 8.2

# Section 8.2 - ≠ If a> 0 the parabola opens upward if...

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Section 8.2 Parabolas and Modeling 1

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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 < 2
Graphing f(x) = a(x - h) 2 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 What happens to when we do these things? 3 2 4 2 4 When 0, the parabola is shifted right h units. When 0, the parabola will be shifted left h units. y x y x y x y a x h y x y x h h = = - = + = - = - = - < 3

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Graphing f(x) = a(x - h) 2 + k ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 What happens to when we do these things? 5 6 2 6 3 7 .25 5 4 When 0, the parabola is shifted up k units. When 0, the parabola will be shifted down k uni y x y x y x y x y a x h k y x y x k k = = + = - = - - = - + = + + = - - - < ts. 4
Vertex Form The vertex form of the equation of a parabola with vertex (h, k) is where a 0 is a constant.

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Unformatted text preview: ≠ If a > 0, the parabola opens upward; if a < 0, the parabola opens downward. 2 ( ) , y a x h k =-+ 5 Identify the vertex. Compare the graph of y = f(x) to the graph of y = x 2 . Then sketch a graph of y = f(x) and y = x 2 in the same xy-plane. Show the transformations. ( 29 ( 29 ( 29 2 2 2 1 1) ( ) 2 2 2) ( ) 3 4 3) ( ) 2 5 3 f x x h x x f x x = --= -+-=-+ 6 Write the vertex form of a parabola that satisfies the conditions given. Assume that a = ±1. a) Opens upward, vertex (-5, 4) a) Opens downward, vertex (3, -8) 7 Write the vertex form of the parabola shown in the graph. Assume a = ±1 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 8 Write the equation in vertex form. Identify the vertex. 2 2 2 1) 4 1 2) 5 4 3) 3 6 1 y x x y x x y x x = + + = +-= -+ + 9...
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Section 8.2 - ≠ If a> 0 the parabola opens upward if...

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