• Feb 12th 2008, 07:22 PM
chaneliman
27x^2- is this a dilation of a factor of 27 from the x intercept and a dilation of 1/27 from the y intercept?
• Feb 12th 2008, 10:12 PM
mr fantastic
Quote:

Originally Posted by chaneliman
27x^2- is this a dilation of a factor of 27 from the x intercept and a dilation of 1/27 from the y intercept?

$\displaystyle g(x) = 27 x^2$ can be considered a transformation of $\displaystyle f(x) = x^2$ in two different ways:

1. $\displaystyle g(x) = 27 f(x)\,$ - dilation by a factor of 27 in the vertical direction, that is, from the x-axis.

2. $\displaystyle g(x) = f(\sqrt{27}x)\,$ - dilation by a factor of $\displaystyle \frac{1}{\sqrt{27}} = \frac{1}{3\sqrt{3}}$ in the horizontal direction, that is, from the y-axis.

1. is the way that most folk would think of it.
• Feb 12th 2008, 11:09 PM
chaneliman
where did the square root come form? for 1/square root 27
• Feb 12th 2008, 11:44 PM
mr fantastic
Quote:

Originally Posted by chaneliman
where did the square root come form? for 1/square root 27

$\displaystyle 27x^2 = (\sqrt{27} x)^2$.

If the second way bothers you, forget you ever saw it. As I said, the first way is how most folk would think of it and is undoubtedly how your teacher would think of it.
The text contains a mathematical question about the transformation of a quadratic function and an answer that explains the transformation in two different ways.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
• Feb 12th 2008, 07:22 PM
chaneliman
27x^2- is this a dilation of a factor of 27 from the x intercept and a dilation of 1/27 from the y intercept?
• Feb 12th 2008, 10:12 PM
mr fantastic
Quote:

Originally Posted by chaneliman
27x^2- is this a dilation of a factor of 27 from the x intercept and a dilation of 1/27 from the y intercept?

$\displaystyle g(x) = 27 x^2$ can be considered a transformation of $\displaystyle f(x) = x^2$ in two different ways:

1. $\displaystyle g(x) = 27 f(x)\,$ - dilation by a factor of 27 in the vertical direction, that is, from the x-axis.

2. $\displaystyle g(x) = f(\sqrt{27}x)\,$ - dilation by a factor of $\displaystyle \frac{1}{\sqrt{27}} = \frac{1}{3\sqrt{3}}$ in the horizontal direction, that is, from the y-axis.

1. is the way that most folk would think of it.
• Feb 12th 2008, 11:09 PM
chaneliman
where did the square root come form? for 1/square root 27
• Feb 12th 2008, 11:44 PM
mr fantastic
Quote:

Originally Posted by chaneliman
where did the square root come form? for 1/square root 27

$\displaystyle 27x^2 = (\sqrt{27} x)^2$.

If the second way bothers you, forget you ever saw it. As I said, the first way is how most folk would think of it and is undoubtedly how your teacher would think of it.
user
The text contains a mathematical question about the transformation of a quadratic function and an answer that explains the transformation in two different ways.

TYPE: SINGLE_QUESTION_WITH_ANSWER