Answers
The evaluation of the functions in the question are as follows;
1. a) [tex]y = \dfrac{1}{x^2+5} -3[/tex]is not a quadratic function
b) The function is a quadratic function
c) The function is a quadratic function
d) The function is a quadratic function
2. Please find attached the graph of the function, y = -2·(x + 3)² + 4, created (for clarity) with MS Excel
a) The axis of symmetry is; x = -3
b) The maximum value is; (-3, 4)
c) The x-intercepts are; √2 - 3, and -√2 + 3
d) y-intercept is (0, -14)
e) The domain is the set of all real numbers
The range is (-∞, 4]
What is a function?A function is a rule that maps an input value unto an output, such that each input has exactly one output.
A quadratic function is a function of the form; y = a·x² + b·x + c
a) The function [tex]y = \dfrac{1}{x^2+5} -3[/tex], when simplified, we get;
[tex]y = \dfrac{1 - 3\cdot x^2 - 15}{x^2+5}[/tex], which is a rational polynomial.
Therefore, the function is not a quadratic function.
b) x² = y - 1
y = x² + 1
The above function is in the form; y = a·x² + b·x + c, where;
a = 1, b = 0, c = 1
c) y = 3·x - 7 + 4·x²
The above function is in the form y = a·x² + b·x + c, where;
a = 4, b = 3, and c = -7
d) The function y = 6·x - 3·√x can be expressed as; √x = z
Therefore; z² = x
Therefore; y = 6·x - 3·√x = 6·z² - 3·z
y = 6·z² - 3·z
The above function is a quadratic function, therefore, the function;
y = 6·x - 3·√3 is a quadratic function
2. The function y = -2·(x + 3)² + 4 is in the vertex form of the equation of a quadratic equation; y = a·(x - h)² + k
Where;
a = The leading coefficient
(h, k) = The coordinates of the vertex
Comparing the values, we get;
The vertex, (h, k) = (-3, 4)
a = -2
When x = 0, we get; y = -2·(0 + 3)² + 4 = -2 × 9 + 4 = -14
With a vertex of (-3, 4), we get;
When x = -6, y = -14
The graph can be obtained by drawing a parabola with vertex at (-3, 4), and passing through the points (0, -14), and (-6, -14)
Please find attached the graph of the function y = -2·(x + 3)² + 4, created with the points (0, -14), (-6, -14), and vertex point (-3, 4), created with MS Excel
a) The axis of symmetry is the line about which the graph is symmetrical
The axis of symmetry is the line x = -3
b) The maximum value is the vertex of the graph, which is the point (-3, 4)
c) The x-intercept are the point the graph intersects the x-axis, which are obtained by plugging in y = 0, as follows;
y = 0 = -2·(x + 3)² + 4
(x + 3)² = -4/(-2) = 2
x + 3 = ±√(2)
x = ±√(2) - 3
The x-intercepts are; x = √2 - 3, and -√2 - 3
d) The y-intercepts are the point the graph intersects the y-axis, which is the point where x = 0
Therefore, the y-intercept is the point (0, -14)
e) The domain is the set of possible input values or x-values
The domain of the function, as presented in the graph is the set of all real numbers
The domain is; (-∞, ∞)
The range is the set of the possible y-values
The graph of the function indicates that the maximum y-value is the point y = 4
Therefore, the range of the function is; -∞ < y ≤ 4, which is (-∞, 4]
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Related Questions
'थूकेंगे' शब्द का वर्ण-विच्छेद कीजिए।
Answers
Answer:
English pls
Step-by-step explanation:
अन्यथा बहस करें, शिकायतें पकड़ें।
PLEASE HELP! URGENT
Answers
50°
Step-by-step explanation:
notice the lines. from that you can tell that 3y+4=5y-10. with calculation, you get y=7. substitute y=7 and you get 50°
If x= 9 in what is the surface area of the geometric shape formed by this net?
Answers
Answer:
D
Step-by-step explanation:
Surface Area = 2×(9×9 + 9×27 + 9×27) = 1134 inches2
I need help please.
Answers
Answer:
b
Step-by-step explanation:
beacause 2x+60 thats the answer
what is 4(z+6)=2965 I need the answer and how you did it
Answers
Answer:
z = 735.25
Step-by-step explanation:
Following steps explain :
[tex]\frac{4\left(z+6\right)}{4}=\frac{2965}{4}\\z+6=\frac{2965}{4}\\z+6-6=\frac{2965}{4}-6\\z=735.25z=\frac{2941}{4}[/tex]
Looks kinda sloppy, but I think you can see what I did :)
#SpreadTheLove <3
what is the area of this parralelogram? h=4 inch b=7 inch
Answers
Answer:
28cm^2
Step-by-step explanation:
4 x 7
Answer:
no sé nada de inglés we ya me entiendes si supiera te ayudará pero eso está difícil busca por internet
Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 times as many villagers as he had in the one before. The game gave Chase 4 villagers to start with. Explain to Chase how to create an equation to predict the number of villagers in any specific town. Then show how to use your equation to solve for the number of villagers he can create to live in his 17th town.
Answers
Answer:
Step-by-step explanation:
a sub n = a sub 1 x r ^ n-1
a sub n = 17 since that's what's in question
a sub 1 = 4 since that's the starting amount
r = 1.13 since that's the difference
a sub 17 = 4(1.13) ^17-1
a sub 17 = 4(7.0673255268)
a sub 17 = 28.2693021072
a sub 17 ≈ 28.37
Please vote brainliest
The number of villagers that Chase can create to live in his 17th town is 28.27.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) As it is given that the number of villagers that Chase had, in the beginning, is 4, and the number of villagers will increase at the rate of 1.13 every time Chase conquers a new village. Therefore, if Chase had n number of towns then Chase had conquered (n-1) number of towns because Chase already had 1 village in the beginning, thus, the villagers will increase (n-1) number of times by the rate of 1.13 times. Therefore, the equation can be written as,
[tex]A = 4(1.13)^{(n-1)}[/tex]
Thus, the function that represents the number of villagers when chase conquered n number of villages is [tex]A = 4(1.13)^{(n-1)}[/tex].
B.) We already know the function that represents the number of villagers, therefore, the number of villagers when Chase had conquered 17 villages can be written as,
[tex]A = 4(1.13)^{(n-1)}\\\\A = 4(1.13)^{(17-1)}\\\\A = 28.27[/tex]
Hence, the number of villagers that Chase can create to live in his 17th town is 28.27.
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A man earns $1500 a week. He saves $500. What percentage did he spend?
Answers
Answer:
3313%
Step-by-step explanation:
Can somebody please answer the question giving brainliest!
Answers
Answer:
A counter clockwise
Step-by-step explanation:
Find the distance between A and B.
A 12 units
B.V106 units
C.9 units
D. 2/12 units
Answers
Answer:
B. [tex] \sqrt{106} [/tex]
Step-by-step explanation:
Distance between A(-4, 3) and B(5, -2) using distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] (-4, 3) = (x_1, y_1) [/tex]
[tex] (5, -2) = (x_2, y_2) [/tex]
Plug in the values into the formula
[tex] d = \sqrt{(5 -(-4))^2 + (-2 - 3)^2} [/tex]
[tex] d = \sqrt{(9)^2 + (-5)^2} [/tex]
[tex] d = \sqrt{81 + 25} [/tex]
[tex] d = \sqrt{106} [/tex]
I Need The Awnsers For This
Answers
Answer: m<2= 126 and is supplementary angle
The ratio of the number of girls to the number of boys in a chess club is 3 to 2. There are 14 boys in the
chess club. What is the number of girls in the chess club?
Answers
Answer:
21 girls
Step-by-step explanation:
3 girls: 2 boys
multiply both sides by 7
21 girls: 14 boys
What is the measure of EACH exterior angle for this regular octagon?
360
45
1080
135
Answers
Answer:
Exterior angle = 45° each
Step-by-step explanation:
Given:
Number of side n = 8
Find:
Exterior angle
Computation:
Exterior angle =360° / n.
Exterior angle =360° / 8
Exterior angle = 45° each
write a real-world problem given the equation 2/3x = 12. Then solve the equation.
please answer it quickly 15 points
Answers
Answer:
x = 1/18
Step-by-step explanation:
2/3x = 12
multiply both sides by 3x
2/3x(3x) = 12(3x)
2 = 36x
x = 1/18
A line segment can intersect a regular hexagon in ________?
1. eight points
2. two points
3. six points
4. four points
Answers
hope this helps
Out of numbers: 5, 7, 21, 25, 28, 35, 42, 56, 75, and 80, choose those which are multiples of 4 or 7
Answers
Answer:
Multiples of 4= 28
Multiples of 7= 7,21,28,35,42
Step-by-step explanation:
I hope this helps, and have a great day! :)
PROINTERENCIAS cuyos RADIOS HIDEN 115m
225m
SON TAN GENJES EXTERIOVENTE ENTRE
OGULOS QUE SE FORAN CUANDO SE UNEN
ros
DE DICHAS CIRCUNFERENCIAS
Answers
Answer: what does this say
Step-by-step explanation:
The weight of water is 62 1/2 lb per cubic foot. Water that weighs 350 lb will fill how many cubic feet?
Answers
The question is worded incorrectly. It should say the DENSITY of water is 62 1/2 lbs per cubic foot. Divide the weight by the density to get volume.
(150 lbs) / (62.5 lbs/ft3) = ? ft3 (the two 3's are exponents. so it'd be ft then an exponent of 3.)
Is the equation 5x = 7x always, sometimes, or never true? Explain.
Answers
Answer:
Step-by-step explanation:
If x = 0, 5x = 7x is true.
If x = 1, 5x ≠ 7x
5x = 7x is sometimes true.
helppppppppppppppppppppp
Answers
We can apply the Pythagorean theorem:
c= (SQ)
a=RQ = 4
b=RS = 4
c²=a²+b²
c=√(16+16)
c=√32
c=4√2
SV=0,5*SQ
SV=0,5*c
SV=√2
4b+5=1+5b
B=____
What do I do....I kinda forgot how to do this...
Answers
Answer:
b = 4
Step-by-step explanation:
4b + 5 = 1 + 5b
4b-5b + 5 = 1
4b-5b = 1 - 5
-b = 1 - 5
-b = -4
-b = -4
b - 4
a $5 bill is exchanged for 72 coins having a total calue.of $5. Some of the coins are nickels and the rest are dimes. How many dimes are in the exchange?
Answers
Hi there!
Ok so we know that every nickel is €5 and every dime is €10...
Let think...
If it is 30 nickels it would be 150 cents and would also be 1.50$...
Now we know that there is 42 dimes left.. let see if it can be equaled.
[tex]42[/tex]·[tex]10=4.62[/tex]
Adding both together would be 6.12 and it’s more than 5$ so this means that the nickels must be more.
Now let think again.. if it would be 44 nickels then the rest for 5.00 would be 2.20 and 72 subtract by 44 is 28. 28 multiply by 10 is perfectly 2.80.. now let check...
[tex]44[/tex]·[tex]5=2.20[/tex]
[tex]72-44=28[/tex]
[tex]28[/tex]·[tex]10=2.80[/tex]
[tex]2.20+2.80=5.00[/tex]
Therefore, the total of dimes would be 28...
6.5.PS-26
Question Help
Nick has an album that holds 700 hockey cards. Each page of the album holds 7 hockey cards. If
72% of the album is empty, how many pages are filled with hockey cards?
FASTTT
Answers
Number of hockey cards in Nick's album = 700
Number of hockey cards in each page of the album = 7
Number of pages in Nick's album :
[tex] = \tt \frac{700}{7} [/tex]
[tex] = \tt100[/tex]
▪︎Thus, the number of pages in Nick's album = 100
Percentage of album that is empty = 72%
Number of pages in the album that is empty :
[tex] = \tt 72\% \: \: of \: \: 100[/tex]
[tex] =\tt \frac{72}{100} \times 100[/tex]
[tex] = \tt \frac{72 \times100}{100} [/tex]
[tex] =\tt \frac{7200}{100} [/tex]
[tex] \color{plum}= \tt72 \: pages[/tex]
▪︎Thus, the number of empty pages in the album = 72
Number of pages in the album that are filled :
[tex] =\tt 100 - 72[/tex]
[tex]\color{plum} = \tt28 \: pages[/tex]
▪︎Therefore :Number of pages filled with hockey cards = 28
heloooo
(-24) + (-25) =
Answers
la respuesta es (-24)+(-25)-49
Answer:
- 49
Step-by-step explanation:
= -24-25(because - and + becomes -)
= -49
At a used bookstore, Cindy bought 2 paperback books for $1.75 and some children's books for $0.75 each,
including tax. She spent a total of $5.75. How many children's books did Cindy buy?
A. 3
B. 4
C. 5
D. 7
Ο Α
B
ос
D
Answers
In a school,2/15 of the students are boys and the rest are girls .If the number of girls is 1950,Find 5he number of boys
Answers
Answer:
300
Step-by-step explanation:
Find the average rate of change
Answers
Answer: The answer to this question would be -6.
I hope this helped!
Answer:
-6
Step-by-step explanation:
g(-3) - g(0) / -3-0
= [2(-3²) + 10] - (0 + 10) ÷ -3
= (28 - 10) / -3
= -18/3
= -6
A map has a scale of 2.5 inches : 4 miles. If two cities are 6 inches away from each other on the map, how far apart are they in real life?
Answers
Answer:
14.4
Step-by-step explanation:
2.5 divided by 6 is 2.4
2.4 x 6 = 14.4
10 pontos
10 points
4. What is the area of the composite figure?
6 cm
9 cm
L
2 cm
10 cm
A. 58 cm
O B. 68 cm
C. 88 cm
D. 48 cm
Answers
Answer:
hope it helped have a good day mate
A college alumni office is choosing a new alumni board of 12 people. They have 25 total applicants.
How many different combinations without repetition of 12 people are there?
Answers
Answer:
5200300
Step-by-step explanation:
Use Combination
25C12=25!/12!(25-12)!The different combinations without repetition of 12 people will be equal to 5,200,300.
What is a Factorial?When a whole number is multiplied by each natural number underneath it, the result is known as its factorial. The symbol "!" can represent the idea of a factorial. As a result, "n factorial" is just n and is defined as the sum of the first n natural integers.
As per the given information in the question,
Total number of people chosen by the board = 12
Total number of applicants = 25
Then the number of combinations without repetition will be = ²⁵C₁₂
= [tex]\frac{25 !}{12!(25-12)!}[/tex]
= 25!/(12! × 13!)
= 5,200,300
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