# How do you find the vertex of y= -x^2+ 4x + 2?

##### 1 Answer
Dec 27, 2017

$- {\left(x - 2\right)}^{2} + 6$

#### Explanation:

−x^2+4x+2

$\implies - 1 \cdot \left[{x}^{2} - 4 x - 2\right]$

$\implies - 1 \cdot \left[\left({x}^{2} - 2 \cdot 2 x + {2}^{2}\right) - {2}^{2} - 2\right]$

$\implies - 1 \cdot \left[{\left(x - 2\right)}^{2} - 4 - 2\right]$

$\implies - 1 \cdot \left[{\left(x - 2\right)}^{2} - 6\right]$

(-(x-2)^2+6)/
The text passage contains a mathematical question about finding the vertex of a parabola, and it provides a step-by-step answer to the question.
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
# How do you find the vertex of y= -x^2+ 4x + 2?

##### 1 Answer
Dec 27, 2017

$- {\left(x - 2\right)}^{2} + 6$

#### Explanation:

−x^2+4x+2

$\implies - 1 \cdot \left[{x}^{2} - 4 x - 2\right]$

$\implies - 1 \cdot \left[\left({x}^{2} - 2 \cdot 2 x + {2}^{2}\right) - {2}^{2} - 2\right]$

$\implies - 1 \cdot \left[{\left(x - 2\right)}^{2} - 4 - 2\right]$

$\implies - 1 \cdot \left[{\left(x - 2\right)}^{2} - 6\right]$

(-(x-2)^2+6)/
user
The text passage contains a mathematical question about finding the vertex of a parabola, and it provides a step-by-step answer to the question.

TYPE: SINGLE_QUESTION_WITH_ANSWER