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
Advocard [28]
3 years ago
12

which statements are true about the graph of the function f(x) = 6x – 4 x2? check all that apply. the vertex form of the functio

n is f(x) = (x – 2)2 2. the vertex of the function is (–3, –13). the axis of symmetry for the function is x = 3. the graph increases over the interval (–3, ). the function does not cross the x-axis.

Mathematics
2 answers:
weeeeeb [17]3 years ago
8 0
A.   The function in vertex form if f(x)=(x-4)^2-1
D.   The y-intercept of the function is (0,5).
E.   The function crosses the x-axis twice. 
Brut [27]3 years ago
5 0

Answer:

The vertex of the function is the point (-3,-13)

The graph increase over the interval--------> (-3,∞)

Step-by-step explanation:

we have

f(x)=6x-4+x^{2}

<u>1) Convert to vertex form</u>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)+4=x^{2}+6x

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)+4+9=x^{2}+6x+9

f(x)+13=x^{2}+6x+9

Rewrite as perfect squares

f(x)+13=(x+3)^{2}

f(x)=(x+3)^{2}-13 -----> function in vertex form

<u>2) Find the vertex</u>

The vertex of the function is the point (-3,-13)

<u>3) Find the axis of symmetry</u>

we know that

In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex

The x-coordinate of the vertex in this problem is equal to x=-3

therefore

the equation of the axis of symmetry is  x=-3

<u>4) Find the increase-decrease intervals</u>

The graph increase over the interval--------> (-3,∞)

The graph decrease over the interval--------> (-∞,-3)

see the attached figure to better understand the problem

<u>5) Find the x-intercepts of the function</u>

we know that

the x-intercepts are the values of x when the value of the function is equal to zero

In this problem the x-intercepts are  

(-6.61,0) and (0.61,0)

so

The function cross the x-axis twice

see the attached figure

You might be interested in
PLEASE HELP! I WILL MAKE YOU BRAINLIST!
Shkiper50 [21]

Answer: A.

Step-by-step explanation: yes

7 0
2 years ago
The shorter leg of a right triangle is 6ft shorter than the longer leg. The hypotenuse is 6ft longer than the longer leg. Find t
vladimir1956 [14]

Answer:

mmm I think you first subtraction

4 0
2 years ago
(15, 0 ) (3,−3)
UkoKoshka [18]
The slope of the line is 1/4
5 0
3 years ago
Read 2 more answers
The price of a DVD is $19 . The price is 12% lower than last week. What was the price of the DVD last week? Round your answer to
nataly862011 [7]

Answer:

The original cost of the DVD was $21`.59

Step-by-step explanation:

In order to find this, you first must note that the new price is 88% of the older price. We get this since there was a subtraction of 12%.

Now knowing that, we can divide the new price by the percentage paid and it will give us the original price.

$19/88% = Original Cost

19/.88 = Original Cost

$21.59 = Original Cost

5 0
2 years ago
What is the average of the following numbers: 18, 64, 23, 78, 82, 91
Katen [24]
To Find The Answer, We Need To Add All Of Them Together, Then Divide By the Number Of Values. So:
64+23+78+82+91
-----------------------
             5

<span>64+23+78+82+91 = 338.
</span>
338
-----
  5

338/5 = 67.6

So, The Average Is 67.6
3 0
3 years ago
Other questions:
  • Togo flew his ultralight plane to a Landing field 30 miles away. With the wind, the flight took three and a half hours.Returning
    13·2 answers
  • Select the TWO correct statements. The product of 3/5 and 4 is greater than 4. The product of 3/5 and 4 is less than 3/5. The pr
    14·1 answer
  • Construct the 99% confidence interval estimate of the population proportion p if the sample size is n=900 and the number of succ
    5·1 answer
  • Harper has $15.00 to spend at the grocery store. She is going to buy bags of fruit that cost $4.75 each and one box of crackers
    5·1 answer
  • How do you find the root of equation x+8=0
    8·2 answers
  • What is 6% of 90?<br><br> I'm bad at percentages
    8·2 answers
  • What is 1 + 1 x 1 -1 / 1 ?
    7·2 answers
  • Greg ran 12 miles a day on 18 different days last month. How many miles did he run?
    6·2 answers
  • Someone please help me
    8·2 answers
  • Consider the Expression
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!