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## Chapter 9

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**Chapter 9**9-1 Symmetry**Chapter 9**9-2 Translations**An alteration of a relation is called a transformation.**Moving the graph of a relation without changing the shape or size is called a translation**Consider the graph of y = |x|, sketch the graphs of the**following by translating**Given the graph of y = x2 use transformations to sketch the**graph of y = (x + 3)2 - 5**The graph of a function is given, sketch the graph under the**given translations (c) Q(x) = f(x – 3) + 2**Chapter 9**9-3 Stretching and Shrinking**Multiplying the function causes the graph to stretch or**shrink vertically**The graph of f(x) is given use the graph to find the graph**of y = 2f(x) The graph of y = 2f(x) is obtained by multiplying each y-value by 2**To get the same y-values, the x-values must be smaller as in**Y2 larger as in Y3**Find the function that is finally graphed after the series**of transformations are applied to the graph of**c**d c a**Chapter 9**9-5 Graphs of Quadratic Functions**A quadratic function has the form**y = ax2 + bx + cwhere a 0.**The highest or lowest point on the**parabola is called the vertex.**In general, the axis of symmetry for the parabola is the**vertical line through the vertex.**Sketch the graph of the following find the vertex, line of**symmetry and the maximum or minimum value: 30. y < x2 31. y x2 32. y -3(x + 3)2**Graphing a Quadratic Function**Graphing a Quadratic Function 1 Graph y= – (x+ 3)2 + 4 2 (–3, 4) 1 a = – , h = –3, and k = 4 2 SOLUTION The function is in vertex form y = a(x – h)2 +k. a < 0, the parabola opens down. To graph the function, first plot the vertex(h, k) = (–3, 4).**Graphing a Quadratic Function**Graphing a Quadratic Function in Vertex Form 1 Graph y= – (x+ 3)2 + 4 2 (–1, 2) (–3, 4) Draw the axis of symmetryx = –3. (–5, 2) Plot two points on one side of it, such as (–1, 2) and (1, –4). Use symmetry to completethe graph. (1, –4) (–7, –4)**Sketch the graph of the following find the vertex, line of**symmetry and the maximum or minimum value: