Answer:
- Horizontal compression, vertical up . . . or ...
- Vertical stretch, vertical up
Explanation:
The transformation to the parent quadratic function can be described either of two ways. For a quadratic, a vertical stretch can also be accomplished by a horizontal compression.
The transformations of interest here are ...
g(x) = a·f(x) . . . . vertical stretch by a factor of 'a'
g(x) = f(a·x) . . . . horizontal compression by a factor of 'a'
g(x) = f(x) +a . . . . vertical translation by 'a' units
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It is easy to see that the parent function f(x) = x^2 has had 9 added to it, so the function has been translated upward 9 units.
The transformation to 3x^2 can be accomplished either of two ways:
3x^2 = 3(x^2) . . . vertical stretch by a factor of 3
3x^2 = (x√3)^2 . . . . horizontal compression by a factor of √3
The attached graph shows either a horizontal compression or a vertical stretch will result in the same graph.
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Additional comment
In the interest of using rational scale factors, we prefer the "vertical stretch, vertical up" description.