The point (4,-2) is the vertex of the graph of a quadratic function. The points (8,6) and (2,0) also fall on the graph of the function.
Part A:Complete the graph of this quadratic function by first finding two additional points on the graph.
Part B:What is the y-intercept of the graph?
Part C:What are the x-intercept?
Part D:Find the interval on which the rate of change is always positive.
Part E:What is the sign of the leading coefficient for this quadratic function? How do you know?
Answers
Answer:
Step-by-step explanation:
y = ax² + bx + c
~~~~~~~
(4, - 2), (8, 6), (2, 0)
a(4²) + b(4) + c = - 2
a(8²) + b(8) + c = 6
a(2²) + b(2) + c = 0
16a + 4b + c = - 2 .............. (1)
64a + 8b + c = 6 ............... (2)
4a + 2b + c = 0 ................. (3)
a = 0.5 ; b = - 4 ; c = 6
y = 0.5x² - 4x + 6
Part A: (0, 6), (6, 0)
Part B: (0,6)
Part C: (6, 0)
Part D: [ 4, ∞ )
The quadratic function has the form f(x) = ax² + bx + c, where a, b, and c are non-zero values, and the calculation of the values can be defined as follows:
Quadratic function:vertex point of graph function= (4,-2)
points= (8,6) and (2,0)
Using the formula of a quadratic function:
[tex]y = ax^2 + bx + c[/tex]
putting the value into the above-given formula:
[tex]\to (4, - 2), (8, 6), (2, 0)\\\\\to a(4^2) + b(4) + c = - 2\\\\\to 16 a + 4b + c = - 2.........................(a)\\\\\to a(8^2) + b(8) + c = 6\\\\\to 64a + 8b + c = 6......................................(b)\\\\\to a(2^2) + b(2) + c = 0\\\\\to 4a + 2b + c = 0................................(c)\\\\[/tex]
Computing the value of a,b, and c:
[tex]\to a = 0.5\\\\ \to b = - 4 \\\\ \to c = 6\\\\[/tex]
Putting the value of a, b, and c values into the quadratic function:
[tex]\to y = 0.5x^2 - 4x + 6[/tex]
So, the calculated points are:
Part A: (0,6)
Part B: (2,0) and (6,0)
Part C: x>4
Part D: positive the parabola upwards
Please find the correct question and graph file in the attachment.Find out more about the quadratic function here:
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Related Questions
140 % of what number is 14?
0.1
19.6
10
0 1,000
Help
Answers
Answer:
10
Step-by-step explanation:
I simply divided 140/14 and got 10! Hope this helps :)
The 140 percentage of the number 10 is 14
Given data ,
To find the number that is 140% of another number, we can set up the equation:
140% of x = 14
So , 140 percentage of the number x = 14
To solve for x, we need to convert 140% to its decimal form, which is 1.40:
1.40 * x = 14
Now we can solve for x by dividing both sides of the equation by 1.40:
x = 14 / 1.40
Dividing 14 by 1.40 gives us:
On simplifying , we get
x = 10
Therefore , the value of x = 10
Hence , 140 percentage of 10 is equal to 14
To learn more about percentage click :
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What the lcm of 12 and 8
Answers
Answer:
24
Step-by-step explanation:
The common multiple that 8 and 12 have in common is 24. This is because 24 is the first multiple of 8 and 12 that is shared
Answer:
The multiples of 8 are: 8, 16, 24, 32, 40, … .
The multiples of 12 are: 12, 24, 36, 48, 60, … .
LCM = 24
Step-by-step explanation:
(PLATO answer)
What is the slope of (-4,6) and (2,-5)
Answers
Answer:
-11/6
Step-by-step explanation:
Slope can be found with this equation:
(y₁ - y₂) / (x₁ - x₂)
What this essentially tells us to do is to put one set of the x and y coordinates into x₁ and y₁, respectfully. Then, put the other set of x and y points as x₂ and y₂.
With this scenerio, we can substitute the given points into the formula.
(6 - (-5)) / (-4 - 2) =
(6 + 5 ) / (-6) =
11 / (-6) =
-11/6
The slope is - 11/6
The answer is -11/6
Tony made $172.50 tutoring last weekend. He tutored for 7 1/2 hours. How much does Tony charge per hour to tutor?
Answers
Answer:
$23 an hour.
Step-by-step explanation:
divide 172.50 by 7.5
How many cubes would it take to fill the box
Answers
Answer:
27359265815502254
Step-by-step explanation:
52758552
The radius of a circle is 10 feet. What is the area of a sector bounded by a 45° arc?
Answers
r=10 m
Hope that helps
Answer:
39.25 square ft
Step-by-step explanation:
[tex]Area \: of \: sector = \frac{45 \degree}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{1}{8} \times 3.14 \times {10}^{2} \\ \\ = \frac{3.14 \times 100}{8} \\ \\ = \frac{314}{8} \\ \\ = 39.25 \: {ft}^{2} [/tex]
?????????????????????
Answers
Answer:
0 and 4
Step-by-step explanation:
Which of the following is equal to the expression listed below?
35 + 14
A.(7+5)(7+2)
B.7(5+2)
C.7+(5 times 2)
D.(7 times 5)(7 times 2)
Answers
B
7(5+2)
= 7(7) = 49
35+14 = 49
2.
There are 300 students in year 8
35% of the students in year 8 walk to school.
How many year 8 students do not walk to school?
Answers
looking for 65% of 300
300 x 65% = 195
195 students don’t walk to school
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PLSSSS SHOWWW THE WORKKK!!!!
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answer: [tex]2^{3} a^{3} b^{12}[/tex]
steps:
you multiply each variable by 3.
example being: 2 x [tex]x^{3}[/tex] is [tex]2^{3}[/tex]
you do this with each of them
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4e + 7e +5
Constants
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Quentin can read 18 pages of a book in 2 hours. How many pages can he read in 10 hours? PLEASE HELP ASAP FOR 17 POINTS!
Answers
Answer:
90 pages in 10 hours :)
Answer:
90 pages
Step-by-step explanation:
First, you need to find the unit rate of how many pages he can read.
So, you divide 18 pages by 2 hours = 9 pages per hour.
Then, you multiply 9*10 hours to find out how many pages he will read in 10 hours.
You get 90.
find the sum of 9a^2/a and 7a^2/a
Answers
Answer:
16a
Step-by-step explanation:
9a^2/a=9a
7a^2/a=7a
9a+7a=16a
Select all the correct answers. Exponential function f is represented by the table. x 0 1 2 3 4 f(x) -12 -4 0 2 3 Function g is represented by the equation. g(x)=-12(1/3)^x Which statements are true about the two functions? Both functions are increasing on all intervals of x. The functions have the same y-intercept. Both functions approach the same value as x approaches ∞. Both functions approach -∞ as x approaches -∞. The functions have the same x-intercept.
Answers
Answer:
Both functions are increasing on all intervals of x: True
Both functions have the same y intercept: True
Both functions approach the same value as x approaches infinity: True
Both functions approach negative infinity as x approaches negative infinity: True.
The functions have the same x intercept: False, they have no x intercept.
Step-by-step explanation:
f(x) is stated to be an exponetial function, hence
[tex]f(x)=ab^{x}[/tex]
f(0) is given as -12, so
-12=a
f(1) is given as -4, so
-4=-12b
b=1/3
This implies that
[tex]f(x)=-12(\frac{1}{3})^{x}[/tex]
g(x) is stated to be
[tex]g(x)=-12(\frac{1}{3})^{x}[/tex]
Conclusion: the functions are identical.
Answer:
so the answers are
the functions have the same y-intercept
both functions approach negative infinity as x approaches infinity
both functions are increasing on all intervals of x
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Answer:
D
Step-by-step explanation:
Find the nouns pls thanks
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Answer:
1.Martin
2.Dining table
3.The children
4.Dishwasher
Step-by-step explanation:
Noun is a name of a person, place, animal, or a thing.
Stay safe, stay healthy and be blessed.
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There are twice as many children as adults attending a family reunion. Which fraction of the family members at the reunion are adults? PLEASE HELP!! I WILL GIVE 18 BRAINLEST POINTS!
Answers
Answer:
1/3
Step-by-step explanation:
let a = adults
so then 2a = children
a/2a(+a) = a/3a
Solve 8W + 20 = 4
How do you solve this equation?
Answers
Answer:
W = -2
Step-by-step explanation:
8W + 20 = 4
=> 8W = 4 - 20
=> 8W = -16
=> W = -16 / 8
=> W = -2
Hope it helps :)
Please mark my answer as the brainliest
Ms. Miller bought burgers for her math students. She paid $39.78 for all burgers. She has 17 students in her class. Choose a variable to represent the cost of one burger, and write an expression for this.
I will give brainliest to the best answer, please answer quickly.
Answers
Answer:
The variable that will represent the cost of one burger will be "b".
The equation is $39.78/17=b
Answer is $2.34
Step-by-step explanation:
Find out how many students she has.
Find out how much she paid for all burgers.
Divide amount she paid for all the burgers by the amount of students she has.
Finally, you have your answer.
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Answer:
I'm pretty sure all except K but i might be wrong
Step-by-step explanation:
Answer:
F and H
Step-by-step explanation:
Im sorry if its wrong
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asap pls
Answers
Answer: He can buy 5 ties
Step-by-step explanation:
12+10=22. 4x5=20. 22+20=42. If you add 1 more tie, you will have $46, so you cannot add one more tie. So the most amount of ties he can buy is 5 ties, with $3 left to spare.
Need help ASAP will give brainliest
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Answer:
Step-by-step explanation:
I think u have the right answer because on the graph im confused how he can spend 100 minutes studying and get lower than one he spent almost 65 minutes less on
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8 cm
+
16.8 cm
Answers
Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
You may get a bit help from this...
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Last Friday Trevon had $29. Over the weekend he received some money for cleaning the attic. He now has $41. How much money did he receive?
A. 29 - n = 41
B. 29 - n = 40
C. 29 + n = 41
D. 29 + n = 40
Answers
Answer:
C
Step-by-step explanation:
Trevon started with $29.
After cleaning, his total rose to $41.
Since he received money, we add that amount (n) to his initial amount of money ($29), to equal his total amount ($41)
One year, the population of a city was 127,000. Several years later it was 129,540. Find the percent increase.
Answers
Answer:
2%
Step-by-step explanation:
Answer: 2%
Step-by-step explanation: Method 1
Express the ending population as a percentage of the starting population:
127000 /129540= 1.02
1.02×100= 102%
Subtract the starting 100% to get the percent increase:
102%−100%= 2%
please hurry. 1. Calculate the grade point average: An A is considered 4.0, a B is 3.0, a C is 2.0, a D is 1.0, and an F is 0. If you received the following grades, what would be your grade point average? Round your answer to the hundredths place. Please show me how you got ur answer step by step
Course Credits Grade
Sociology 3.0 A
Calculus 4.0. F
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Answers
Answer:
b
Step-by-step explanation:
Anyone know the answer !
Answers
Answer:
Step-by-step explanation:
An adult earthworm was measured to be 31.5 inches long. (Yes, they really can be that
size!)
1 inch = 2.54 cm
100 cm = 1 m
Use the information above to convert this length into meters (m). (Round your answer
to the nearest hundredth.)
Answers
Answer:
0.80m
Step-by-step explanation:
first, convert the measurement into centemeters
31.5 x 2.54
=80.01cm
to convert cm to m divide the answer by 100
80.01/100
=0.8001
then round the answer to the nearest hundredth
=0.80m
2. Write the matching multiplication fact. 7 + 7 + 7
Answers
Answer:
3x7
Step-by-step explanation:
7 + 7 + 7 is 3 x 7 because 7x3=21 and 7+7+7=21