Find an equation in standard form of the parabola passing through the points (1, -2), (2, -2), (3, -4)?
Answers
9514 1404 393
Answer:
y = -x^2 +3x -4
Step-by-step explanation:
We are given two points with the same y-value, so we know the axis of symmetry lies halfway between their x-coordinates, at ...
x = (1 +2)/2 = 3/2
Then the vertex form of the equation can be written ...
y = a(x -3/2)^2 +k
__
We can use two of the points to find the values of 'a' and 'k'.
For (x, y) = (1, -2)
-2 = a(1 -3/2)^2 +k = a/4 +k
For (x, y) = (3, -4)
-4 = a(3 -3/2)^2 +k = 9a/4 +k
Subtracting the first of these equations from the second, we have ...
(9a/4 +k) -(a/4 +k) = (-4) -(-2)
2a = -2
a = -1
Then k can be found from the first equation.
-2 = -1/4 +k
k = -1 3/4
So, the vertex form equation is ...
y = -(x -3/2)^2 -7/4
__
Expanding this, we can find the standard form.
y = -(x^2 -3x +9/4) -7/4)
y = -x^2 +3x -4
Related Questions
Savannah loves to talk on her cell phone. She has $100 in her budget to pay this month’s cell phone bill. Her cell phone plan is $20 per month plus $0.10 per minute of usage. If x represents the minutes of usage, which equation best represents the word problem?
A. 100+20=.10x
B. 100+.10x=20
C. 20 +.10x=100
D. 20-.10x= 100
Answers
Answer: C. best fits the word problem.
Step-by-step explanation:
The reason C. best fits is because the bare minimum $20 she has to pay plus .10 times whatever amount of minute's she spends talking has to equal $100 for her to stay in budget. A good example would be say she spends 800 minutes in total on her phone. 0.10 times 800 is 80. So in this hypothetical situation, it would be 20 + 80 = 100.
The triangle shown below is translated 5 units down and 3 units to the left. What are the coordinates of the vertices of the translated triangle? * D 2 3 4 O (2.0), (2-1), and (-1,-4) O (2,10).(-2,9), and (-1, 11) 0 (0,2).(-4,1), and (-3,-2) 0 (0,8).(-4,7), and (-3, 4)
Answers
Answer:
Where's the picture?
Step-by-step explanation:
Sam drove 315.5 miles in 5 hours. If he drove the same number of miles each hour, how many miles did he drive per hour?
Answers
Answer:
63.1
Step-by-step explanation: You divide 315.5 by 5 to get the answer
Answer:
Step-by-step explanation:
it should be 315.5 or since it is and a 5 all you have to do is multiply it easy hope this helped :)
3(x + 3) + 2x + 6 = 45
Solve the equation
Answers
Answer:
x = 6
Step-by-step explanation:
3(x + 3) + 2x + 6 = 45
3x + 9 +2x + 6 = 45
5x + 15 = 45
5x = 30
x = 6
For the function f(x) = x + 4, what is the ordered pair for the point on the graph where x = 3p?
Answers
Answer:
D. (3p, 3p + 4)
Step-by-step explanation:
Answer:
(3p, 3p + 4)
Step-by-step explanation:
-5 – 5 + (6 x -7) x 2
Answers
Answer:
-94
Step-by-step explanation:
Helpppppppppppppppp meeeee asap
Answers
Answer:
18,27, putting 3 fives instead of 5 3s.
Step-by-step explanation:
Point S is between points R and T on RT. Use the information to write an equation in terms of x. Then solve the equation and find RS, ST, and RT.
RS = 2x - 8
ST = 3x - 10
RT = 17
RS =
ST=
RT=
Answers
Answer:
RS=6
ST=11
Step-by-step explanation:
answer is above
The value of x is 7 and the measure of the line segment RS is 6 units, ST = 11 units, and RT = 11 units
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Point S is between points R and T on RT.
RS = 2x - 8
ST = 3x - 10
RT = 17
From the above information:
RT = RS + ST
17 = 2x - 8 + 3x - 10
17 = 5x - 18
35 = 5x
x = 35/5
x = 7
RS = 2x - 8 = 2(7) - 8 = 6 units
ST = 3x - 10 = 3(7) - 10 = 11 units
RT = 17 units
Thus, the value of x is 7 and the measure of the line segment RS is 6 units, ST = 11 units, and RT = 11 units.
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What is the area and the circumference of a circle with the diameter 8 m
Answers
Answer:
the area is 50.27 meters squared
Step-by-step explanation:
A toy glider plane is launched from a height of 50 feet above the ground. If the plane descends at a constant rate of 1.3 feet per second, then its height, in feet, after s seconds can be found using the equation h = 50-1.3s. Use the equation to find the height of the glider 9 seconds after it was launched.
Answers
Answer:
38.3 feet
Step-by-step explanation:
h=50-1.3(9)
h=50-11.7
h=38.3
1) Relacione o nome dos polígonos de acordo com o total de lados. a) Triângulo ( ) 8 lados. b) Quadrilatero ( ) 6 lados. c) Pentágono ( ) 7 lados. d) Hexágono ( ) 3 lados. e) Heptágono ( ) 4 lados. f) Octógono ( ) 5 lados. 2) O ângulo reto , também conhecido como ângulo de um quarto de volta mede:. a) 90° b) 180° c) 270 ° d) 360 ° 3) O ângulo que mede menos 90 ° e mais de 0° é chamado de : a) agudo b) raso c) reto d) obtuso. 4) Um teatro 64 fileiras de poltronas e cada fileira tem 35 poltronas. Qual é a lotação desse teatro? 5) André e Federico fizeram 28 pacotes contendo 180 bandeirinhas cada pacote . Quantas bandeirinhas os meninos fizeram ? 5) Calcule : a) 861 x 27= b) 798 x 45=
Answers
Answer:
1
O nome de um polígono é um nome que se deve ao número de lados que o polígono possui.
a) Triângulo = 3 lados.
b) Quadrilátero = 4 lados.
c) Pentágono = 5 lados.
d) Hexágono = 6 lados.
e) Heptágono = 7 lados.
f) Octógono = 8 lados.
2) O ângulo reto, também conhecido como ângulo de um quarto de volta, mede: a) 90 °
3) O ângulo que mede menos 90 ° e mais que 0 ° é denominado: a) agudo
4) 2240
5) 5040 sinalizadores
6) Calcule: a) 861 x 27 = 23247
b) 798 x 45 = 35910
Step-by-step explanation:
1) Liste o nome dos polígonos de acordo com o número total de lados.
a) Triângulo = 3 lados.
b) Quadrilátero = 4 lados.
c) Pentágono = 5 lados.
d) Hexágono = 6 lados.
e) Heptágono = 7 lados.
f) Octógono = 8 lados.
2) O ângulo reto, também conhecido como ângulo de um quarto de volta, mede: a) 90 ° b) 180 ° c) 270 ° d) 360 °
= a) 90°
Um triângulo ângulo reto pode ser definido como um triângulo onde um de seus 3 ângulos é equivalente a 90 graus (90°).
3) O ângulo que mede menos 90 ° e mais que 0 ° é denominado: a ) agudo b) raso c) reto d) obtuso.
Um ângulo maior que 0 ° e menor que 90 ° pode ser definido como um ângulo agudo.
= a) agudo
4) Um teatro com 64 filas de assentos e cada fila tem 35 assentos. Qual é a capacidade deste teatro?
No teatro, cada fila tem 35 lugares.
Temos 64 linhas
O número total de licenças que temos é calculado como:
1 fila = 35 assentos
64 linhas =
Multiplicação cruzada
64 filas × 35 assentos
= 2.240 assentos.
Portanto, a capacidade do teatro é de 2240.
5) André e Federico confeccionaram 28 embalagens contendo 180 bandeiras cada embalagem. Quantas bandeiras os meninos fizeram?
O número de bandeiras que os meninos fizeram é calculado como:
28 pacotes × 180 bandeiras
= 5040 sinalizadores
6) Calcule: a) 861 x 27 = 23247
b) 798 x 45 = 35910
What expression shows the greatest common factor correctly factored from the expression 12a2−36ab+18b2?
Answers
Answer:
Factor each coefficient into primes
Step-by-step explanation:
The Factor expression shows the greatest common factor correctly factored from the expression 12a2−36ab+18b2 is each coefficient into primes.
What is expression?1a: an action, procedure, or instance of representing something in a medium (like words): freedom of expression in speech. b This gift is meant to show how much I like you. (1): something that represents, embodies, or manifests another. (2): an important phrase or term.A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11 written as 8 + 3.The Factor expression shows the greatest common factor correctly factored from the expression 12a2−36ab+18b2 is each coefficient into primes.To learn more about expression refer to:
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3(k - 5) + 9k 2-3 does anyone know how to solve this?
Answers
Answer:
=21k-18
Step-by-step explanation:
Hello!! I need help with square root please help me!!!
Answers
Ok so what you need to do is you need to get all the numbers and see which one is the right number so...
A. y = 11.2 that is wrong
B. y = 25 is wrong
C. y = 5 is right
D. y = 15 is wrong.
C is right because it would be 5 times 5 times 5. SO 5 times 5 is 25, and then u times it by 5 and you get 125!
C is correct
Hope this helps!!
Answer:
This is actually a cube root, since you need a cube root to cancel out the cube.
C, y = 5
Step-by-step explanation:
125 = 5 × 5 × 5 = 5^3
5 × 5 × 5 = 25 × 5 = 125.
Therefore the cube root of 125 = 5.
It REALLY helps when you break these into factors.
[tex] \sqrt[3]{125} = 5 , \: as \: {5}^{3} \: = 125 [/tex]
This is essentially asking what multiplied by itself three times is equal to 125.
Process of elimination can be used for any number cubed that is ≠ 125
i.e : 11.2^3 ≠ 125
11.2^3 = 11.2 × 11.2 × 11.2 = (11.2-1.2)(11.2+1.2)(11.2) = (11.2)((10)(12.4) + 1.2^2) = 124 + 1.44 = (125.44)(11.2) = 125.44(10+1+(2/10)) = 1254.4 + 125.44 + 25.088 = 1404.928 ≠ 125, y ≠ 11.2
I.e : 25^3 = 25 × 25 × 25 = 625 × 25 = (600+25)(25) = 625 + 6(25)(100) = 15000 + 625 = 15625 ≠ 125, y ≠ 25.
And i.e: 15^3 = 15 × 15 × 15 = 225 × 15 = (225)(10+5) = 225(10) + 225(10/2) = 2250 + 2250/2 = 2250 + 1125 = 3375 ≠ 125, y ≠ 15.
Determine the intercepts of the line.
y= -3.6 +12
y-intercept:
X-intercept:
Need to know NOW
Answers
Answer:
y = 12
x = 10/3
Step-by-step explanation:
y = -3.6x + 12
From this equation, which is in slope intercept form (y = mx+b), we already know that b represents the y-intercept, so that means the y-intercept is 12.
To find the x-intercept, we need to make y equal 0 to find x. So:
0 = -3.6x + 12
-3.6x = -12
x = 3.33333 --> 3 1/3
x = 10/3
x-intercept: 10/3
y-intercept: 12
Steps:
Finding x
y=-3.6x+12
0= -3.6x+12
3.6x=12
x=10/3
Finding y
y=-3.6x+12
y=-3.6(0)+12
y=12
help with math problems
Answers
Answer:
Step-by-step explanation:
b. 27
d 25
e 20
f 342
h 54
For an upcoming field trip, there will be 36 fifth graders and 48 sixth graders. Each van will carry the same number of students, and only students from one grade. If each van will carry the greatest possible number of students, how many vans will be needed?
Answers
Answer:
7 Vans will be needed
Step-by-step explanation:
You move up 4 units and right 2 units. You end at (-1, 3). Where did you start?
Answers
Answer:
You started at (-3,-1)
Gianna walked 12 miles in 6 hours. What was her walking rate in miles per hour?
Answers
Answer:
2 mph
Step-by-step explanation:
12/6
Her walking rate in miles per hour is 2
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
Given;
Gianna walked 12 miles in 6 hours
6hours= 12 miles
1hour= 12/6miles
1hour= 2miles
Therefore, the rate of gianna by unitary will be 2mph
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Is (5, 7) a solution to the equation y = x + 2?
Answers
Answer:
5 + 2 = 7.
Step-by-step explanation:
If you mean the other way around then no.
2 + 7 doesn't equal 5.
Answer:
Yes i agree- 5+2=7 if you mean it that way
Step-by-step explanation:
If a pair of lines is intersected by Third line known as a transversal, then pairs of congruent angles are formed true or false
Answers
Answer:
true
Step-by-step explanation:
it forms eight angles
PLEASE BE QUICKKK!!
Answers
Answer:
The Answer would be C, i think
Step-by-step explanation:
At Break Time Bakery, donuts are 0.75 each and drinks cost $1.50 each. Which equation best represents y, total cost of purchasing x number of donuts and a drink?
Answers
Answer: B
Step-by-step explanation:
Answer:
B.)y = 1.50x + .75
Step-by-step explanation:
Jada is planning a kayak trip. She finds an expression for the time, T(s), in hours it takes her to paddle 10 kilometers upstream in terms of s, the speed of the current in kilometers per hour. This is the graph Jada gets if she allows s to take on any value between 0 and 7.5. What would be a more appropriate domain for Jada to use instead?
Answers
Answer:
A more appropriate domain would be all real numbers except x = 5.5
Step-by-step explanation:
Given that the domain of a rational function consists of the set of real numbers but excluding those real numbers that results in a zero in the denominator
The given graph of the function has a vertical asymptote at s = 5.5 which indicates a value for which the function is not defined and at x = 5.5, and as such the value (5.5) of the asymptote is not a member of the function's domain
The values of the domain of a function consisting of a reciprocal must exclude does that result in a zero denominator.
The domain of the function that represents Jada's trip is the set of input value the function can take
The appropriate domain is: all real numbers except x = 5.5
From the graph, we can see that:
The x-value starts at negative infinity, and ends near 5.5The x-value then continues near 5.5, and ends at positive infinityThis means that the input of the graph cannot be 5.5
Hence, an appropriate domain would be: [tex]\mathbf{x \ne 5.5}[/tex]
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The ratio of boys to girls in vonzells class is 2:3. Which of the following represents the number of boys and girls in her class? Pleaseeeee helppp meeeee.
Answers
Answer:
2 is boy and 3 is girl
Step-by-step explanation:
cauze in first place boy is plced so it is 2.
and in second place girl is placed so it is 3.
Answer:
A) 10:15
Step-by-step explanation:
both are x5
You are 5 1/4 feet tall. You must be at least 5 3/4 feet tall to ride a roller coaster. Which inequality represents how much taller you must be to ride the roller coaster?
Answers
Answer:
Not quite understanding but it could possibly be 5 1/4<5 3/4.
5 1/4 + 1/2= 5 3/4= 5 3/4
Step-by-step explanation:
It takes 12 men 5 days to complete a job
Work out how many days it would take 3 men to complete the same job
Answers
Answer: 8
Step-by-step explanation: i took the test
1.25 days would be taken for 3 men to complete the same job.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that 12 men 5 days to complete a job
We have to find for how many days three men can complete the same job.
Let x be the time taken by 3 men to complete the job.
Formulate a proportional equation.
12/5=3/x
Apply cross multiplication
12x=15
Divide both sides by 12
x=15/12
both 15 and 12 are multiples of 3
x=5/4
x=1.25
Hence, 1.25 days would be taken for 3 men to complete the same job.
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The distance between two asteroids was calculated at 37,500,000,000 kilometers. What is this value expressed in scientific notation?
Answers
Quadrilateral KLMN was reflected across y = -2. Find M.
Answers
Answer:
The picture states it is reflected across y = -x, which is different to y = -2 (maybe the question before's answer was 2? However this question is not linked)
If it is y = -x, the answer is (1, 1)
If it is y = -2, which I doubt, the answer is (-1, -3)
The circumference of a circle is 10 inches. What is its area in square inches?
Answers
Answer:
7.96 square inches.
Step-by-step explanation:
Area of a circle given a circumference is given by formula:
[tex]A = \frac{C^{2}}{4\pi}[/tex]
So substituting into equation we have: [tex]C= 10[/tex].
Therefore [tex]A = 10^{2}/4\pi = 100/4\pi=25/\pi =7.96[/tex] square inches.
The area of the circle is 7.96 square inches if the circumference of a circle is 10 inches.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that:
The circumference of a circle is 10 inches.
As we know the circumference of a circle is given by:
C = 2πr
C is the circumference of the circle.
r is the radius of the circle.
10 = 2πr
r = 5/π inches
As we know,
The area of the circle is given by:
A = πr²
Here, A represents the area of the circle.
Plug the value of the radius r in the above formula:
A = π(5/π)²
A = 25/π square inches
Take π = 3.14
A = 25/3.14
A = 7.96 sqaure inches
Thus, the area of the circle is 7.96 square inches if the circumference of a circle is 10 inches.
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