february 7, 2014 - weebly€¦ · february 7, 2014 generalizations for the function y = a(x - p) 2...
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February 7, 2014
February 7, 2014
Which of the following describe a quadratic function?
a) f : x 3x2 b) g : x 2x3 - 5
c) y = 2x2 - x + 1 d) f(x) = 3x - 1x
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February 7, 2014
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February 7, 2014
February 7, 2014
February 7, 2014
February 7, 2014
February 7, 2014
February 7, 2014
February 7, 2014
Generalizations for the function y = a(x - p) 2 + q:
1. Axis of symmetry is the line x = p.
2. Coordinates of the vertex are (p, q)
3. The value of " a" controls the shrinking and stretching as well as direction of opening, " p" controls the horizontal shifts and "q" controls the vertical shifts.
4. If a > 0, the minimum value of y is at y = q. If a < 0, the maximum value of y is at y = q.
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3.1
Example 1: Your Turn
Determine the following characteristics for each function.• the vertex• the domain and range• the direction of opening• the equations of the axis of symmetryThen, sketch each graph.
a) y = (x – 2)2 – 4 b) y = –3(x + 1)
2 + 3 A
nsw
er P
art a
Ans
wer
Par
t b
February 7, 2014
3.1
Example 1: Your Turn
Determine the following characteristics for each function.• the vertex• the domain and range• the direction of opening• the equations of the axis of symmetryThen, sketch each graph.
a) y = (x – 2)2 – 4 b) y = –3(x + 1)
2 + 3
Ans
wer
Par
t b
3.1
Example 1: Your Turn
Determine the following characteristics for each function.• the vertex• the domain and range• the direction of opening• the equations of the axis of symmetryThen, sketch each graph.
a) y = (x – 2)2 – 4 b) y = –3(x + 1)
2 + 3 A
nsw
er P
art a
Ans
wer
Par
t b
February 7, 2014
y = 1/3(x - 5)2- 4
February 7, 2014
3.1
Example 2: Your Turn
Ans
wer
Determine a quadratic function in vertex form for each graph.
a) b)
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2 a) f (x) = 0.8x2 - 32 a) f (x) = 0.8x
2 - 3
3.1Example 3
1 Determine the number of x-intercepts a quadratic function hasby examining• the value of a to determine if the graph opens upward or downward• the value of q to determine if the vertex is above, below, or on the x-axis
Determine the Number of x-Intercepts Using a and qDetermine the number of x-intercepts for each quadratic function.a) f (x) = 0.8x
2 – 3 b) f (x) = 2(x – 1)
2 c) f (x) = –3(x + 2)
2 – 1
Continue Next Page
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3.1 Example 3 Continued
44 c) f (x) = –3(x + 2)2 – 1
3 b) f (x) = 2(x – 1)2