
Concept explainers
To describe and graph the contrast in the pair of functions.

Explanation of Solution
Given information :
Given functions are y=12x2 and y=3x2 .
Graph :
Interpretation :
The graph of quadratic function f(x) when multiplied by a positive constant a , the resulting graph af(x) is a vertical dilation of f(x) . The function is stretched or compressed vertically by a factor of |a| .
If |a| >1 , the graph of f(x) is stretched vertically, that is, all points on the graph f(x) move farther away from the x -axis.
If |a| <1 , the graph of f(x) is compressed vertically, that is, all points on the graph f(x) move closer to the x -axis.
In the function y=12x2 , the value of |a| <1 at a=12 . Thus, the transformation of f(x) when multiplied by a , as seen in the graph, is that it is compressed vertically by a factor of 12 .
The graph of quadratic function f(x) when multiplied by a positive constant a , the resulting graph af(x) is a vertical dilation of f(x) . The function is stretched or compressed vertically by a factor of |a| .
If |a| >1 , the graph of f(x) is stretched vertically, that is, all points on the graph f(x) move farther away from the x -axis.
If |a| <1 , the graph of f(x) is compressed vertically, that is, all points on the graph f(x) move closer to the x -axis.
In the function y=3x2 , the value of |a| >1 at a=3 . Thus, the transformation of f(x) when multiplied by a , as seen in the graph, is that it is stretched vertically by a factor of 3 .
Therefore, as seen in the graph, the contrast of the function y=12x2 to the graph of y=3x2 is that the latter is vertically stretched by a factor of 6 when compared to the former.
Chapter 9 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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