1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Crazy boy [7]
3 years ago
6

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

urth) squared + thirteen-eighths y = negative 6 (x minus one-fourth) squared + nineteen-eighths y = negative 6 (x minus one-half) squared + seven-halves
Mathematics
2 answers:
mart [117]3 years ago
7 0

Answer:

y  = -6(x - \frac{1}{2})^2 -\frac{7}{2}

Step-by-step explanation:

Given:

y = -6x^2 + 3x + 2

Required

Rewrite in vertex form

The vertex form of an equation is in form of: y = a(x - h)^2+ k

Solving: y = -6x^2 + 3x + 2

Subtract 2 from both sides

y - 2 = -6x^2 + 3x + 2 - 2

y - 2 = -6x^2 + 3x

Factorize expression on the right hand side by dividing through by the coefficient of x²

y - 2 = -6(x^2 + \frac{3x}{-6})

y - 2 = -6(x^2 - \frac{3x}{6})

y - 2 = -6(x^2 - \frac{x}{2})

Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

<em>Rough work</em>

The coefficient of x is \frac{-1}{2}

It's square is (\frac{-1}{2})^2 = \frac{1}{4}

Adding inside the bracket of -6(x^2 - \frac{x}{2}) to give: -6(x^2 - \frac{x}{2} + \frac{1}{4})

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: -6(\frac{1}{4})

------------------------------------------------------------------------------------

The expression becomes

y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})

y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})

y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})

Factorize the expression on the right hand side

y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2

y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2

y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2

y - (\frac{7}{2})= -6(x - \frac{1}{2})^2

y  +\frac{7}{2} = -6(x - \frac{1}{2})^2

Make y the subject of formula

y  = -6(x - \frac{1}{2})^2 -\frac{7}{2}

<em>Solved</em>

Nutka1998 [239]3 years ago
7 0

Answer

Y= -6( x - 1/2)^2 + 7/2

Step-by-step explanation:

Edg 2020 drop a brainliest bruh

You might be interested in
The point of the concurrence of all angle bisectors of a triangle is called the?
wolverine [178]

Answer:

Incenter is the answer.

Hope it helps!!!

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a comp
Andre45 [30]

Answer:look it up

Step-by-step explanation:

5 0
3 years ago
Which term is the question
Pani-rosa [81]

Answer:

trinomial

Step-by-step explanation:

Given polynomial has three terms, therefore it is a trinomial.

7 0
3 years ago
Find the value of x such that the data set has the given mean. 98, 123, 105, 114, 109, x ; mean 113 x = (Type an integer or a de
kotykmax [81]

Answer: 129

Step-by-step explanation:

the mean is the average of the data. including x, there are 6 data points

average = total/6

average = (98 + 123 + 105 +114 +109 + x) / 6

113 = (98 + 123 + 105 +114 +109 + x) / 6

113 = (549+ x) / 6

678 = 549 + x

x = 129

6 0
2 years ago
Assume the upper arm length of males over 20 years old in the United States is approximately Normal with mean 39.2 centimeters (
MAVERICK [17]

Answer:

The interval [32.6 cm, 45.8 cm]

Step-by-step explanation:

According with the <em>68–95–99.7 rule for the Normal distribution:</em>  If \large \bar x  is the mean of the distribution and s the standard deviation, around 68% of the data must fall in the interval

\large [\bar x - s, \bar x +s]

around 95% of the data must fall in the interval

\large [\bar x -2s, \bar x +2s] 

around 99.7% of the data must fall in the interval

\large [\bar x -3s, \bar x +3s]

So, the range of lengths that covers almost all the data (99.7%) is the interval

[39.2 - 3*2.2, 39.2 + 3*2.2] = [32.6, 45.8]

<em>This means that if we measure the upper arm length of a male over 20 years old in the United States, the probability that the length is between 32.6 cm and 45.8 cm is 99.7%</em>

3 0
3 years ago
Other questions:
  • The supplementary angle of 100.6° is
    9·1 answer
  • Which equation shows an example of the associative property of addition? (–7 + i) + 7i = –7 + (i + 7i) (–7 + i) + 7i = 7i + (–7i
    14·2 answers
  • Express the following relationship as a rate.
    7·1 answer
  • Factor completely 81x^4-16
    5·2 answers
  • Witch list orders the number from least to greatest ​
    15·1 answer
  • Only one question .Who knows about this plz "Find the measures indicated. round to the nearest tenth".​
    15·2 answers
  • Select the correct answer.
    10·2 answers
  • AHH I SHALL GIVE U POINTS FOR THIS CAUSE I AM LAZY AND DON'T WANNA DO IT ON MY OWN
    8·2 answers
  • The value of a + b + c for equation 2 Y - x = 7 is ​
    6·1 answer
  • What’s the length of AZ. If A is between Y and Z, Y A = 22, AZ = 16x, and Y Z = 166
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!