5.1 Stretching & Reflecting Quadratic Relations.notebook

5.1 Stretching & Reflecting Quadratic Relations.notebook
2015 04 16
April 16, 2015
Ch. 5: Applying Quadratic Models
Getting Started:
Terms:
Translation ‐ the result of sliding each point on a shape the same distance in the same direction
shift‐ left/right, up/down
Reflection ‐ the result of flipping a shape to produce a mirror image of the shape
Transformation ‐ the result of moving or changing the size of a shape according to a rule
stretch/compression
Concepts:
Read P. 246, Example 1, Question 2, Assignment: Practice 5,6,8bc
1
5.1 Stretching & Reflecting Quadratic Relations.notebook
April 16, 2015
5.1 Stretching/Reflecting Quadratic Relations
factored: y=a(x‐r)(x‐s)
standard: y=ax2+bx+c
a>0 opens up
a<0 opens down
Vertical Stretching ‐ a transformation that increases all the y‐
coordinates of a relation by the same factor
Vertical Compression ‐ a transformation that decreases all the y‐
coordinates of a relation by the same factor
The affect that a has on the graph of y = ax2
• when a > 1, the graph is stretched vertically by a factor of a.
• when a < ‐1, the graph is stretched vertically by a factor of a and reflected across the x‐axis See Example 1, P.252/3
• when 0 < a < 1, the graph is compressed vertically by a factor of a.
• when ‐1 < a <0, the graph is compressed vertically by a factor of a and reflected across the x‐axis See Example 2, P.253/4/5 2
5.1 Stretching & Reflecting Quadratic Relations.notebook
April 16, 2015
Sketch the graph of the equation y = 3x2 by transforming the graph of y=x2.
y=x2
y = 3x2
3
5.1 Stretching & Reflecting Quadratic Relations.notebook
April 16, 2015
p. 256
Assigned Work
pp.256‐258 # 2abc, 4cd, 5ac, 6, 11
4
5.1 Stretching & Reflecting Quadratic Relations.notebook
April 16, 2015
5
5.1 Stretching & Reflecting Quadratic Relations.notebook
April 16, 2015
6