Answers
Step-by-step explanation:
I guess we are only talking about quadratic functions/equations here.
the world is not unified regarding what is the standard form of a quadratic equation.
but let's assume your teacher means
standard form
f(x) = y = ax² + bx + c
vertex form
f(x) = y = a(x - h)² + k
so, we are using the provided x, y coordinates to get a, b and c.
3.75 = a×0.125² + b×0.125 + c
3 3/4 = a×(1/8)² + b×(1/8) + c
15/4 = a/64 + b/8 + c
15×16/64 = a/64 + 8b/64 + 64c/64
=> 240 = a + 8b + 64c
4 = a×0.25² + b×0.25 + c
4 = a×(1/4)² + b×(1/4) + c
4 = a/16 + b/4 + c
4×16/16 = a/16 + 4b/16 + 16c/16
=> 64 = a + 4b + 16c
3 = a×0.5² + b×0.5 + c
3 = a×(1/2)² + b×(1/2) + c
3 = a/4 + b/2 + c
3×4/4 = a/4 + 2b/4 + 4c/4
=> 12 = a + 2b + 4c
we have now from the third equation
a = 12 - 2b - 4c
we put this into the second equation
64 = (12 - 2b - 4c) + 4b + 16c = 12 + 2b + 12c
32 = 6 + b + 6c
26 = b + 6c
b = 26 - 6c
and therefore
a = 12 - 2(26 - 6c) - 4c = 12 - 52 + 6c - 4c = 2c - 40
this a and b we use now in the first equation
240 = (2c - 40) + 8(26 - 6c) + 64c =
= 2c - 40 + 208 - 48c + 64c = 18c + 168
72 = 18c
c = 4
b = 26 - 6×4 = 26 - 24 = 2
a = 12 - 2×2 - 4×4 = 12 - 4 - 16 = -8
so, the standard form is
f(x) = y = -8x² + 2x + 4
the vertex form
we get this by transforming the standard form.
e.g. by competing the square :
y - 4 = -8x² + 2x = -8(x² - x×1/4)
y - 4 -8×(1/8)² = -8(x² -x×1/4 + (1/8)²)
y - 4 - 8/64 = -8(x - 1/8)²
y - 32/8 - 1/8 = -8(x - 1/8)²
y - 33/8 = -8(x - 1/8)²
y = -8(x - 1/8)² + 33/8
Related Questions
find the value of x and y.
Answers
Answer:
[tex]x=13[/tex]
[tex]y=23[/tex]
Step-by-step explanation:
[tex](12x - 41) + 5x = 180[/tex]
[tex]12x + 5x = 180 + 41[/tex]
[tex]17x = 221[/tex]
[tex] \frac{17x}{17} = \frac{221}{17} [/tex]
[tex]x = \frac{221}{17} [/tex]
[tex]x = 13[/tex]
[tex](12 \times 13 - 41) + 5(13) = 180[/tex]
[tex]115 + 65 = 180[/tex]
[tex]180 = 180[/tex]
[tex]vertical \: angles[/tex]
[tex](12x - 41) = 5y[/tex]
[tex]12 \times 13 - 41 = 5y[/tex]
[tex]115 = 5y[/tex]
[tex] \frac{115}{5} = \frac{5y}{5} [/tex]
[tex]y = \frac{115}{5} [/tex]
[tex]y = 23[/tex]
[tex]5y=12x-41[/tex]
[tex]5×23=12×13-41[/tex]
[tex]115=115[/tex]
We can use the two terms in x to find the value of x.
Angles on a line have a sum of 180°
⇒ (12x -41)° + 5x° = 180°
⇒ (12x + 5x -41)° = 180°
⇒ 17x° = 180 + 41°
⇒ x = 13
We can use the same principle of angles to find y
5x° + 5y° = 180°
since x = 13; 5(13) + 5y = 180
5y = 115
y = 23
∴ x = 13 & y = 23(4y+3)-(2y-9) help plz
Answers
Answer:
2y+12
Step-by-step explanation:
(4y+3)-(2y-9)
Distribute the minus sign
4y+3-2y+9
Combine like terms
4y-2y +3+9
2y + 12
Which of the following three-dimensional geometrical shape do not have a curved surface?
A. Cylinder
B. Cone
C. Sphere
D. Prism
Answers
Answer:prism
Step-by-step explanation:
Evaluate the expression when m= -4. m² +5m +1
Answers
Answer:
-3
Step-by-step explanation:
Plug in m = -4 in the expression,
m² + 5m + 1 = (-4)² + 5*(-4) + 1
= 16 - 20 + 1
= -4 + 1
= - 3
Answer:
-3
Step-by-step explanation:
(-4)×(-4)+5×(-4)+1
16-20+1
-3
find how many six-digit numbers can be formed from the digits 2, 3, 4, 5, 6 and 7 (with repetitions), if: the numbers formed must be even
Answers
Answer:
3
Step-by-step explanation:
there are only 3 even numbers
Samuel earns $10 per hour plus $1 per T-shirt he sells. Find his earnings when he works 8 hours and sells 20 T-shirts.
Answers
Answer:
$100
Step-by-step explanation:
$10(8hrs)=$80
$1(20)=$20
=$100
Hope this helps!! :)
10 •8 =80
20•1=20
80+20= 100
PLEASE HELPP
Can you please put how you worked it out?
4x+3-x=12x-15
Answers
Answer:
2
Step-by-step explanation:
4x+3−x=12x−15
Combine 4x and −x to get 3x.
3x+3=12x−15
Subtract 12x from both sides.
3x+3−12x=−15
Combine 3x and −12x to get −9x.
−9x+3=−15
Subtract 3 from both sides.
−9x=−15−3
Subtract 3 from −15 to get −18.
−9x=−18
Divide both sides by −9.
x= –18÷–9
Divide −18 by −9 to get 2.
x=2
Which of the following graphs is a function?
a.
c.
COF
d.
b.
A
Next
Submit
Save and Exit
Mark this and return
Answers
Answer:
The answer is D I believe
1/9 divided by 8/7 this is called dividing fractions
Answers
Answer:
True?
Step-by-step explanation:
Which rays are perpendicular.
1. OA and OD
2. OA and OB
3. OA and OC
4.OA and OF
Answers
Amanda read 15 pages of her 150-page book in 2 hours at this rate how long will it take her to read the entire book
Answers
7.5 pages per 1 hour
150 divided by 7.5
20 hours
Work out the height of this triangle with base,
b
= 8.6mm and area,
A
= 256.28mm2.
Answers
Answer:
[tex]59.6[/tex] mm
Step-by-step explanation:
We know that the base times the height divided by two is the area, so we have that [tex](8.6*h)/2=256.28[/tex].
We can multiply both sides by [tex]2[/tex] to get [tex]8.6*h=512.56[/tex].
Lastly, we divide by [tex]8.6[/tex] on both sides to get [tex]h=512.56/8.6[/tex].
This simplifies to [tex]\boxed{h=59.6}[/tex] mm!
7x + 12 = 26
what does x equal
Answers
Answer:
x=2Step-by-step explanation:
Hope this helps :}
Pls mark brainliest :P
And have an amazing day <3
Ok but why are so many people doing face reveals on this app?!? Anyways…
Answers
Answer:
bru its cool
Step-by-step explanation: lol
A.f(x)=500(0.05)^x
B. f(x)=500(1.05)^x
C. f(x)=500+50x
D. f(x)=500x+50
Answers
Answer:
a
Step-by-step explanation:
diego and lin are dinking milkshakes lin started with 12 ounces and drinks 1/4 ounces per second . deigo starts with 20 ounces and drinks 2/3 ounce per second how long will it take lin and diego to finish their milk shakes
Answers
Answer:
lin: 12 ounces/ (1/4) ounces= 12/(1/4)=48 sec
diego:20 ounces/ (2/3) ounces= 20/(2/3)= 30 sec
Suppose a line graphed on a coordinate plane represents the distance traveled in miles by an automobile as a function of time in hours. Assuming that the relationship between time and distance traveled is proportional, which of these statements is correct? Select one that applies.
A. If the automobile was going 30 mph, the slope of the line is.
C. If the automobile was going mph, the y-intercept of the line is
D. If the automobile was going mph, the y-intercept of the line is.
E. If the automobile was going mph, the y-intercept of the line is.
Answers
Using linear function concepts, it is found that the correct option is:
A. If the automobile was going 30 mph, the slope of the line is 30.
A linear function is modeled by an equation in the following format:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.In this problem, the relationship between time and distance traveled is proportional, which means that slope is given by the velocity. Thus, the correct option is:
A. If the automobile was going 30 mph, the slope of the line is 30.
A similar problem is given at https://brainly.com/question/16302622
Answer:
a
Step-by-step explanation:
Can I get some help? Maybe from a fellow student or teacher that knows how to help with Clever? For some reason, whenever I'm trying to get into Clever, I press the login button but it takes me to this page saying something went wrong and when I click Sign In (Second picture) it stays on that page. This happened on Wednesday too, and by the time I had the email to send to my Teacher, I was able to get back in. (That time it had taken me a whole hour) I've also already tried restarting my computer too.
I'LL GLADLY GIVE BRAINLIEST TO THE PERSON WHO CAN HELP ME
Answers
Answer:
honestly, this happened to me so i clear my cache and cookies and deleted my search history and it worked
to clear cache and cookies (for chrome) go to the top right of your bookmarks bar.
there will be three tiny dots going vertical(up and down)
click on it
there will be a dropdown menu
the third to the bottom will say settings
click that
then when you are i settings, click on advanced dropdown menu(it will be on the left hand side of the screen towards the bottom)
press restore settings to their original defaults
all your cookies and cache will be deleted
your extensions will be deactivated(but not deleted dont worry)
restart your computer and then go to your history and delete everything
restart chrome and you shoul be good
Brainliest?Which set of numbers does not include -8?
Whole numbers
Integers
Rational numbers
Opposites of whole numbers
Answers
Answer:
Whole numbers, and rational numbers
Step-by-step explanation:
7 1) = -2 y - y -6 -5 -3 X
Answers
7/2 is the slope and (-2,0) is the starting point.
On each of maggie's bird-watching trips,she has seen at least 24 birds.If she has taken 4 of these trips each year over the past 16 years,at least how many birds has maggie seen
Answers
Answer:
Step-by-step explanation:
24 birds per year for 4 years for the past 16 years would be 24 x 4 x 16 = 1,536
At least 1,536 birds
Gina works in a bookstore and was entrusted
the task of counting how many books there are
math. She observes that there is a total
of 5 estates, each shelf has 5 divisions
of books, each of these divisions has 5
sections with 5 books. How many books are there in
the math section?
Answers
5 • 5 • 5 • 5 =
25 • 25 =
625
Consider if the following Infinite Series converges or diverges; If converges, find the sum.
[tex] \displaystyle \large{ 1 + 2 + \frac{1}{2} - \frac{2}{3 } + \frac{1}{4} + \frac{2}{9} + \frac{1}{8} - \frac{2}{27} + ...}[/tex]
Please show your work too. Thanks!
Answers
Step-by-step explanation:
You can immediately notice that the sum consists of the sum of two infinitely decreasing geometric progressions[tex]\displaystyle \large \boldsymbol {} \underline1+\underline 2+\underline {\frac{1}{2}} -\frac{2}{3} +\underline {\frac{1}{4}} -\frac{2}{9} +\underline{\frac{1}{8}} -\frac{2}{27} + \ldots = \\\\\\ \underbrace{\bigg(1+2+\frac{1}{2} +\frac{1}{4} \ldots \bigg)}_{\rm \big S_2}-2 \underbrace{\bigg(\frac{1}{3}+\frac{1}{9} +\frac{1}{27} \ldots \bigg)}_{\big S_3}[/tex] The formula for an infinitely decreasing geometric progression:[tex]\displaystyle \large \boldsymbol { \rm S=\frac{b_1}{1-q} \ \ ; \ \ |q|<1}[/tex] Where : q -denominatorb₁ -is the first member of the progressionThen:Denote the sum of the numbers in the first bracket for S₂ ; and in the second bracket for S₃[tex]\displaystyle \large \boldsymbol {} \rm S_2=\frac{2}{1-\dfrac{1}{2} } =\frac{2}{\dfrac{1}{2} } =4 \\\\\\\ S_3=\frac{\dfrac{1}{3} }{1-\dfrac{1}{3} } = \dfrac{1}{\dfrac{3}{\dfrac{2}{3} } } =\frac{1}{2}[/tex] Substitute the values : [tex]\large \boldsymbol {} \rm S_2-2S_3=4- 2\cdot \dfrac{1}{2} =\boxed{3}[/tex]7 + 3(1 - 2x) HELP ASAP
Answers
Answer:
The solution is −6+10.
Step-by-step explanation:
Please help me find the value of x
Answers
Answer:
the answer to x is 15 degrees
Answer:
x = 15
Step-by-step explanation:
these two labeled angles are supplementary because they are same-side interior angles
we can add them together and set the sum equal to 180 to find 'x'
3x - 15 + 150 = 180
combine -15 and 150 to get 135
3x + 135 = 180
subtract 135 from each side to get:
3x = 45
divide each side by 3 to get:
x = 15
It is hard and i need help
Answers
Answer:
what help ok i answer it because im genius ok
What makes a ghost grumpy?
Answer: The rain. It really dampens their spirits!
I’m really sorry if you didn’t find that funny..No hate please!✌
I’m confused on how to solve this
-3.1a+0.5=6.39
Answers
(-1.9x(-3.1)+0.5=6.39
A= -1.9
Burwell Bank is offering to double your money! They say that if you invest with them at 8% interest compounded monthly, they will double your money. If you invest $3500 in the account, how long will it take for your money to double?
Answers
Answer:
350000% is the answers
Step-by-step explanation:
sana maka tulong
can u plz help me with this
Answers
Answer:
x = 61, y = 29
Step-by-step explanation:
29+x = 90
x = 61
x + y = 90
y + 61 = 90
y = 29
90-29=61
y=29
90-61=29
i’m confused on how to solve
what’s the area??
Answers
Step-by-step explanation:
see the attached file
the area of pentagon is shown