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
AlexFokin [52]
3 years ago
14

Which statements about the graph of the function f(x) = -x2 - 4x + 2 are true? Select three options.

Mathematics
1 answer:
Nady [450]3 years ago
8 0

Answer:

Domain is all real numbers.

The range is \{y|y\le 6\}

The function is increasing over (-\infty,-2).

The function is decreasing over (-2,\infty)

The function has a positive y-intercept.

-----------------This is a guess if I had interpreted your choices correctly:

Second option: The range is \{y|y\le 6\}

Third option:  The function is increasing over (-\infty,-2).

Last option:  The function has a positive y-intercept.

I can't really read some of your choices. So you can read my above and determine which is false. If you have a question about any of what I said above please let me know.

Note: I guess those 0's are suppose to be infinities? I hopefully your function is f(x)=-x^2-4x+2.

Step-by-step explanation:

f(x)=-x^2-4x+2 is a polynomial function which mean it has domain of all real numbers.  All this sentence is really saying is that there exists a number for any value you input into -x^2-4x+2.

Now since the is a quadratic then it is a parabola. We know it is a quadratic because it is comparable to ax^2+bx+c, a \neq 0.

This means the graph sort of looks like a U or an upside down U.

It is U, when a>0.

It is upside down U, when a.

So here we have a=-1 so a which means the parabola is an upside down U.  

Let's look at the range.  We know the vertex is either the highest point (if a) or the lowest point (if a>0).

The vertex here will be the highest point, again since a.

The vertex's x-coordinate can be found by evaluating \frac{-b}{2a}:

\frac{-(-4)}{2(-1)}=\frac{4}{-2}=-2.

So the y-coordinate can be found by evaluate -x^2-4x+2 for x=-2:

-(-2)^2-4(-2)+2

-(4)+8+2

4+2

6

So the highest y-coordinate is 6.  The range is therefore (-\infty,6].

If you picture the upside down U in your mind and you know the graph is symmetrical about x=-2.

Then you know the parabola is increasing on (-\infty,-2) and decreasing on (-2,\infty).

So let's look at the intevals they have:

So on (-\infty,-2) the function is increasing.

Looking on (-4,\infty) the function is increasing on (-4,-2) but decreasing on the rest of that given interval.

The function's y-intercept can be found by putting 0 in for x:

-(0)^2-4(0)+2

-0-0+2

0+2

2

The y-intercept is positive since 2>0.

You might be interested in
A jar contains 4 blue marbles, 6 red marbles, 10 purple marbles, and 5 green marbles. If you choose one marble, what is the prob
Paladinen [302]
It be a 3/4 possibility that it won’t be green
6 0
3 years ago
Which expression represents the product of s and 39?<br>A=39-s<br>B=39÷s<br>C=39s<br>D=39+s​
Degger [83]
The answer would be c because it means Multiply and whenever a variable is next to a number in this case 39s then that means it a multiplication
So C. 39s
4 0
2 years ago
A TV that usually sells for $174.97 is on sale for 20% off. If sales tax on the TV is 5%, what is the price of the TV, including
OlgaM077 [116]

The answer is basically easy. It’s $126.84.

4 0
2 years ago
Read 2 more answers
A swimming pool fills 1/10 of the pool in 1/5 of an hour. At this rate, how long does it take to fill up the pool? Show ALL your
Cloud [144]

Answer:

i got 20 hours

Step-by-step explanation:


7 0
2 years ago
5.40 is 9% of what price? Please show step by step
Rama09 [41]
p\%=\dfrac{p}{100}\\\\9\%=\dfrac{9}{100}=0.09\\\\9\%\ of\ x\ is\ 5.4\to0.09x=5.4\ \ \ \ |divide\ both\ sides\ by\ 0.09\\\\\boxed{x=60}
3 0
3 years ago
Other questions:
  • Can someone help me solve 5(t+2) please
    13·1 answer
  • Julie spend 5.62 dollars at the store. Micah spends 5 times as much as Julie. Jermy spends 6.72 more than micah. How much money
    5·2 answers
  • 50 POINTS!!!!!!
    12·1 answer
  • Please help me in the question above? Please!!
    10·1 answer
  • What is the recursive rule for this geometric sequence? 27,  9,  3,  1,  ... Enter your answers in the boxes.
    13·2 answers
  • If you multiply me by 2, I become a number greater than 20 and less than 40 who am I
    10·1 answer
  • canstanza has 13 blue envelopes she has 3 fewer yellow envelopes then blue envelopes she has 7 times as many green envelopes as
    15·2 answers
  • To make lemonade, i use a ratio of $7$ parts water to $1$ part lemon juice. if i want to make a gallon of lemonade, and there ar
    11·2 answers
  • A consumer advocacy group wants to determine whether there is a difference between the proportions of the two leading automobile
    5·1 answer
  • Select ALL the correct answers.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!