Question

What type of transformation occurred if the quadratic parent function becomes y = 3x² + 9

Horizontal compression, vertical up

Vertical stretch, vertical up

Horizontal stretch, vertical down

Vertical compression, vertical down

Answer 1

Horizontal compression, vertical up

Explanation:

The 3 compresses the parent function

The 9 moves it up 9 Spaces

Answer 2

• 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.