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: