# What is the answer for question 4.a)? (Draw 2) http://postimg.org/image/q8ectggh3/

Posted on

The picture represents a parabola that opens upward, hence a>0, whose vertex (h,k) is at (3,-7), hence, you may write the equation of the corresponding quadratic function, such that:

`f(x) = a(x - h)^2 + k`

Considering a = 1 yields:

`f(x) = (x - 3)^2 - 7`

You need to represent the graph of transformed function `y = f(x - 3) + 5` , based on the graph of original function, such that:

- move vertically the red graph up 5 units: `y = f(x) + 5 => y = (x - 3)^2 - 7 + 5 => y = (x - 3)^2 - 2`

- shift the graph 3 units to the right, such that: `y = (x - 3 - 3)^2 - 2 => y = (x - 6)^2 - 2`

Hence, sketching the graph of transformed function `y = f(x - 3) + 5 = (x - 6)^2 - 2 ` yields:
The text passage describes a math problem involving a parabola and its transformation, but the actual question is not fully provided in the text. The passage provides an answer to a transformation problem.
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
# What is the answer for question 4.a)? (Draw 2) http://postimg.org/image/q8ectggh3/

Posted on

The picture represents a parabola that opens upward, hence a>0, whose vertex (h,k) is at (3,-7), hence, you may write the equation of the corresponding quadratic function, such that:

`f(x) = a(x - h)^2 + k`

Considering a = 1 yields:

`f(x) = (x - 3)^2 - 7`

You need to represent the graph of transformed function `y = f(x - 3) + 5` , based on the graph of original function, such that:

- move vertically the red graph up 5 units: `y = f(x) + 5 => y = (x - 3)^2 - 7 + 5 => y = (x - 3)^2 - 2`

- shift the graph 3 units to the right, such that: `y = (x - 3 - 3)^2 - 2 => y = (x - 6)^2 - 2`

Hence, sketching the graph of transformed function `y = f(x - 3) + 5 = (x - 6)^2 - 2 ` yields:
user
The text passage describes a math problem involving a parabola and its transformation, but the actual question is not fully provided in the text. The passage provides an answer to a transformation problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER