Chapter 10-‐2: Graphs of Quadra-c Func-ons Part 2 Ver-cal Stretch/Compression If you ________________ the parent function ______________ by ________ to make it _________________, then you have _________________ the graph ________________. Let’s see what this looks like:

f (x) = x 2

f (x) =

1 2 x 2

f (x) = 2x 2

Example 1: Graph

f (x) = 3x 2 . State the transformation. Give the vertex, domain, and range.

Graph

f (x) =

2 2 x . State the transformation. Give the vertex, domain, and range. 3

Ver-cal Flip If you ________________ the parent function ______________ by ________ to make it _________________, then you have _________________ the graph ________________. Example 2: Graph

f (x) = −2x 2 . State the transformation. Give the vertex, domain, and range.

Graphing in Vertex Form If a quadratic function is written in the form ___________________, it is in _______________ form. Properties: 1. It has vertex ___________ and the vertical line ____________ is the axis of symmetry. 2. The graph opens ______ if ___________ and ___________ if ____________. 3. The graph is _____________ than ______________ if __________________. The graph is _____________ than ______________ if __________________. Example 3: Decide whether each parabola opens up or down and whether it is wider or narrower than the graph of

f (x) = x 2 .

(a)

2 f (x) = − x 2 3

(b)

f (x) =

(c)

f (x) = −2x 2 − 3

(d)

f (x) = 3x 2 + 2

3 2 x +1 4

Example 4: Graph

f (x) =

1 (x âˆ’ 2)2 + 1 . Give the vertex, domain, and range. 2

Using your Calculator to find a Quadratic Model for Data Steps to Finding a Quadratic Regression 1. 2. 3. 4. 5. 6.

Open a new document. Insert a table. type data into table. Use an x value that would make sense. Insert a Data and Statistics page. For the y-axis, use the dependent variable. For the x-axis, use the independent variable. Press Menu - Analyze - Regression - Show Quadratic

Example 5: The table below lists the number of Americans (in thousands) who are expected to be over 100 years old for selected years. [Source: US Census Bureau.] How many Americans will be over 100 years old in the year 2008? (a) Using this data, find a quadratic function that models the situation.

Year

(b) If this trend continued, how many Americans were over 100 years old in 2008?

Number (thousands)

1994

50

1996

56

1998

65

2000

75

2002

94

2004

110

Assigned Problems: pg. 615 #2, 3-9 (mult 3), 15, 19, 21, 27, 33, 44, 45, 47, 50