Find the vertex, axis of symmetry, y intercept of each parabola. State the number of x intercepts. Then sketch the graph of each function. f(x)=2(x-4)^2+4
Answers
Answer:
Vertex: [tex](x,y) = (4,4)[/tex], Axis of symmetry: [tex]x = 4[/tex], no x-Intercepts, y-Intercepts: [tex](x,y) = (0, 36)[/tex]. The graph is represented in the image attached below.
Step-by-step explanation:
The equation of the parabola in vertex form and whose axis of symmetry is vertical is described by this formula:
[tex]y - k = C\cdot (x-h)^{2}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]C[/tex] - Vertex constant.
[tex]h, k[/tex] - Coordinates of the vertex.
By direct comparison, we find the following information:
[tex]h = 4[/tex], [tex]k = 4[/tex], [tex]C = 2[/tex]
Vertex
The vertex is a point of the parabola so that [tex](x,y) = (h, k)[/tex].
If we know that [tex]h = 4[/tex] and [tex]k = 4[/tex], then the coordinates of the vertex are [tex](x,y) = (4,4)[/tex].
Axis of symmetry
The axis of symmetry is a line of the form [tex]x = h[/tex].
If we know that [tex]h = 4[/tex], then the axis of symmetry is [tex]x = 4[/tex].
To find the x and y intercepts, we need to transform the equation of the parabola into its standards, which is a second grade polynomial:
[tex]y - k = C\cdot (x-h)^{2}[/tex]
[tex]y - k = C\cdot (x^{2}-2\cdot h\cdot x +h^{2})[/tex]
[tex]y = C\cdot x^{2} -2\cdot C\cdot h \cdot x + (C\cdot h^{2}+k)[/tex]
If we know that [tex]h = 4[/tex], [tex]k = 4[/tex] and [tex]C = 2[/tex], then the equation of the parabola in standard form is:
[tex]y = 2\cdot x^{2}-16\cdot x + 36[/tex]
x-Intercepts
The x-intercepts of the polynomial (if exist) can be found by the Quadratic Formula:
[tex]x_{1,2} = \frac{16\pm \sqrt{(-16)^{2}-4\cdot 2\cdot (36)}}{4}[/tex]
[tex]x_{1,2} = 4 \pm \frac{\sqrt{-32}}{4}[/tex]
[tex]x_{1,2} = 4 \pm i \,\frac{4\sqrt{2}}{4}[/tex]
[tex]x_{1,2} = 4 \pm i\,\sqrt{2}[/tex]
As both roots are conjugated complex numbers, there are no x-intercepts.
y-Intercepts
The y-intercept (if exists) can be found by evaluating the polynomial at [tex]x = 0[/tex]:
[tex]y = 2\cdot 0^{2} - 16\cdot 0 + 36[/tex]
[tex]y = 36[/tex]
The y-intercept is [tex](x,y) = (0, 36)[/tex].
Lastly, we proceed to plot the function by using graphing tools.
Related Questions
what is the direction of the vector line w = (-1,6)
Answers
Answer:
Step-by-step explanation:
direction=y-component/x-component
tan theta =6/-1
tan theta=-6
theta=[tex]tan^{-1}[/tex]-6
theta=180 -80.53
theta=99.47°
therefore the direction of the given vector line is 99.47°
A rectangular room’s length is 2 feet less than its’ width and the area of the room is 120 ft^2
Use the formula A= length* width
a. Write algebraic expressions for the length and width .
b. Write an algebraic equation for the area of the room.
c. Solve the equation by factoring and give the dimensions of the room.
Answers
Answer:
a. 120/w = l
120/l = w
b. l times w = 120
Step-by-step explanation:
Step-by-step explanation:
120/W=1
120/W= I
I =W is equal to 10
1. What is the value of x?
A. 21
B. 41
C. 22
D. 20
Answers
Answer:
I think the answer is 20!!!!!
Explanation:I did this before
pleassssssssssssssssssssss help marking as brainlist
Answers
Answer:
C. 32 3/8
Step-by-step explanation:
First, divide the fraction and the 4 into two equations. This makes 7 x 4 and 7 x 5/8. Then multiply both to get 28 and 35/8. Then convert 35/8 into a mixed number to get 4 3/8. Then add 28 + 4 3/8 to get 32 3/8.
Answer:
it would be choice 3
3⅜
Step-by-step explanation:
hope it helps you :)
What is the equation of the asymptote for the exponential function shown on the graph?
Answers
Answer:
B) y=0
Step-by-step explanation:
The exponential function shown has a horizontal asymptote at the line y=0, which means that y will approach 0 as the value of x decreases. Therefore, B is correct.
The figure below shows some angles what is the measure of L ABD?
A, 46
B, 56
C, 90
D, 100
Answers
Answer:
90
Step-by-step explanation:
The expression wA - 36 is equivalent to
Answers
Answer:
4. (w² + 6)(w² - 6)
Step-by-step explanation:
w^4 - 36
(w² + 6)(w² - 6)
Help
Nxhxhxhdhdhdbsbsbdhdhd
Answers
a bag contains 517.6 g of dollar coins. Each coin has a mass of 8.1 g
Answers
Answer:
63 coins
Step-by-step explanation:
I am going to assume you are asking how many dollar coins are in the bag, I apologize if I am wrong.
So first, set up the problem. The total number is 517.6 and each coin weighs 8.1
So you would divide 517.6 by 8.1 to get 63.9012346 (which has too many decimal points so round)
But rounding up would get the wrong number because it would be too light for the amount of coins said to be in there, but rounding down gives you 63.
So 63 times 8.1 is 510.3 and the total could consider the weight of the bag into the total 517.6.
how many cm are in 4metres
Answers
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ᵗᵒᶠᵘ ˡᵒᵍᵍᶦⁿᵍ ᵒⁿ…
⊹˚ʚ ❑Answer︰400 centimeters!!
✎Daily reminder: make sure to eat food and stay hydrated, have a good day :D
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Given that √5=2.24 and √7.07, find the value of
(a) √0.05
(b)√0.0005
(c)√0.5
(d)√0.005
Answers
Answer:
0.05 = 5/100
sqrt(0.05] = sqrt(5/100) = sqrt(5)/sqrt(100) = 2.24/10 = 0.224
0.0005 = 5/10000
sqrt [0.0005) = sqrt(5/10000) = sqrt(5)/sqrt(10000) =
= 2.24/100 = 0.0224
0.5 = 50/100
sqrt(0.5) = sqrt(50/100) = sqrt(50)/sqrt(100) = 7.07/10 =
= 0.707
0.005 = 50/10000
sqrt(0.005) = sqrt(50/10000) = sqrt(50)/sqrt(10000) =
= 7.07/100 = 0.0707
Step-by-step explanation:
it would be nice, if you could truly type the full and real question.
you mean sqrt(50) = 7.07
right ?
this assumption leads to the answers above.
A 45 gram sample of a substance that's used to sterilize surgical equipment has a
K-value of 0.1483.
Find the substance's half-life, in days. Round your answer to the nearest tenth.
Answer:
Answers
Answer:
t = 4.7 days
Step-by-step explanation:
The half life formula is
N = No * e ^ (-kt)
Where No is the initial amount of the substance
N = 45 e ^ (-.1483 t)
We want 1/2 of the substance left
22.5 is half of 45 grams
22.5 = 45 e ^ (-.1483 t)
Divide each side by 45
1/2 = e ^ (-.1483 t)
Take the natural log of each side
ln(1/2) = ln (e ^ (-.1483 t))
ln(1/2) = -.1483t
Divide each side by -.1483
ln(1/2) / -.1483 = t
t=4.67395
Rounding to the nearest tenth
t = 4.7 days
Can you please solve this answer ...
Answers
9514 1404 393
Answer:
∠SPR = 48°
Step-by-step explanation:
The relevant relations are ...
an inscribed angle is half the measure of the arc it interceptsa triangle inscribed in a semicircle is a right trianglean exterior angle is equal to the sum of the remote interior angles of a triangleSince PR is a diameter, triangle PQR is a right triangle with angle PQR being the right angle.
This makes ∠PRQ complementary to ∠RPQ:
∠PRQ = 90° -28° = 62°
Exterior angle RTS is the sum of interior angles TRQ and TQR, so angle TQR can be found to be ...
110° = 62° +∠TQR
∠TQR = 110° -62° = 48° = ∠SQR
__
Angle TQR, also angle SQR, subtends arc SR, so is the same measure as angle SPR, which also subtends the same arc.
∠SPR = 48°
I could use some help on this
Answers
Answer:
the answer is B
68. Find the volume of this square-based
pyramid. (meters)
A. 810 m2
B. 270 m2
C. 405 m3
D. 180 m3
E. 60 m
Answers
Answer:
270 m^2
Step-by-step explanation:
1. Write down your formula. It is V= 1/3 Bh
2. Plug in your numbers. Your new formula is V= 1/3 (81)(10)
3. Simplify the expression to get 270.
Are the only bases that I need to use 2 and 4 along with the height 2.5 and I just ignore the 3?
Answers
Answer:
[tex]7.5\ units^2[/tex]
Step-by-step explanation:
The formula to find the area of a trapezoid is the following,
[tex]A=(h)(\frac{(b_1)+(b_2)}{2})[/tex]
Where ([tex]h[/tex]) represents the heights of the trapezoid, ([tex]b_1[/tex]) and ([tex]b_2[/tex]) represent the bases of the trapezoid, or rather the two parallel sides of the trapezoid.
One is given all of these values in the picture,
[tex]h = 2.5\\\\b_1 = 2\\\\b_2 = 4[/tex]
Substitute these values into the formula and solve for the area of the trapezoid,
[tex]A=(2.5)(\frac{(2)+(4)}{2})[/tex]
Simplify,
[tex]=(2.5)(\frac{6}{2})\\=(2.5)(3)\\=7.5[/tex]
Which of the following values of y will result in a true statement when substituted into the given equation?
y + 4.2 = 3.4
A. y = -0.8
B. y = 2.2
C. y = 4.3
D. y = 5.2
Answers
Answer:
A. -0.8
Step-by-step explanation:
non of the other answers will work because they are positive.
Answer:
A, y = -0.8
Step-by-step explanation:
To solve this, you have leave the y alone.
Subtract 4.2 from both sides.
y + 4.2 - 4.2 = 3.4 - 4.2
y = 3.4 - 4.2
y = -0.8
I need a fast reply please
Answers
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \:A. \:- 8 {b}^{4} + 10 {b}^{3} + 10b}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex](7b + 7 {b}^{3} - 6 {b}^{4} ) + (3 {b}^{3} + 3b - 2 {b}^{4} )[/tex]
➼[tex] \: 7b + 7 {b}^{3} - 6 {b}^{4} + 3 {b}^{3} + 3b - 2 {b}^{4} [/tex]
Combining like terms, we have
➼[tex] \: - 6 {b}^{4} - 2 {b}^{4} + 7 {b}^{3} + 3 {b}^{3} + 7b + 3b[/tex]
➼[tex] \: - 8 {b}^{4} + 10 {b}^{3} + 10b[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
What is the solution set for -2n – 2 > 2?
Answers
Answer:
n < -2
Step-by-step explanation:
-2n – 2 > 2
-2n (– 2 + 2) > 2 + 2
-2n > 4
-2n/-2 > 4/-2
n < -2
The sum of two numbers is 24 and their difference is 8. What is the smaller of the two numbers?
Answers
24-8 (difference) = 16
16/ 2 numbers = 8 is smallest number
8 + 8(difference) = 16 is largest number
The smaller number is 8
Step-by-step explanation:
everything can be found in the picture
a package of buttons contains 6 red 3 blue and 7 white P(white buttons) Calculate the probability of the event
Answers
Match each expression with its sum or difference
Answers
Answer:
1-4=-3
-1-4=-5
-1+4=3
1-|-4|=5
Answer:
[tex]1-4=-3\\-1-4=-5\\-1+4=3\\1-(-4)=5[/tex]
Step-by-step explanation:
The hardest part about negative numbers in addition is remembering when to add, rather than subtract. In the last equation, we add the numbers together, because the negative sign cancels out with subtraction. All of the other equations we can follow exactly what it says to do, because there are no minus signs right next to each other.
Find the value of x in Oo
12
X
10
X
(Simplify your answer.)
Enter your answer in the answer box and then click Check Answer
All parts showing
Clear All
Answers
Answer:
x = 8
Step-by-step explanation:
To get x, we will use the pythagoras theorem;
10² = x² + (12/2)²
100 = x² + 6²
100 = x² + 36
100 - 36 = x²
64 = x²
Swap
x² = 64
x =√64
x = 8
Hence the value of x is 8
Jorge y Noelia van a jugar al "4 en línea". Si el tiempo de una partida es de 2 minutos y 30 segundos, ¿cuántas partidas podrían jugar durante 25 minutos?
Answers
Answer:
Pueden jugar 10 partidas en 25 minutos.
Step-by-step explanation:
Sabemos que el tiempo de una partida es:
t = 2min + 30 seg
Queremos saber cuantas partidas se pueden jugar en un total de 25 minutos.
Esto es simplemente igual a la cantidad de veces que podemos "meter" 2 minutos y 30 segundos en 25 minutos, que está dado por el cociente:
N = (25 min)/(2min + 30 seg)
Pero para resolver esto, primero tenemos que tener todos nuestros valores en las mismas unidades.
Sabiendo que 60 se = 1 min
entonces:
30 seg = (30/60) min = 0.5 min
Entonces podemos reescribir:
t = 2 min + 30 seg = 2 min + 0.5 min = 2.5 min
Ahora podemos resolver el cociente:
N = (25 min)/(2.5 min) = 10
Esto significa que pueden jugar 10 partidas en 25 minutos.
solve for x round to the nearest tenth if necessary
Answers
Answer:
Step-by-step explanation:
take 60 degree as reference angle
using cos rule
cos 60 = adjacent / hypotenuse
1/2 = 80/x
do cross multiplication
2*80 = x
160 = x
160.0 = x
What is an equivalent expression to 6(a+b)?
Answers
Answer:
6a+6b
by distributive property
Step-by-step explanation:
Answer:
6a+6b
Step-by-step explanation:
6(a+b)
Use the distributive property to multiply 6 by a+b.
6a+6b
Rahal is adding the Epression below. -3+[(-7)+(-6)] First he rewrites the expression. [3+(-7)]+(6) Which number property did Rashal use to rewrite the expressio?
Answers
Note: The second expression must be [tex][(-3)+(-7)]+(-6)[/tex] instead of [tex][3+(-7)]+(6)[/tex]
Given:
The given expression is:
[tex]-3+[(-7)+(-6)][/tex]
Rahal rewrites the expression as:
[tex][(-3)+(-7)]+(-6)[/tex]
To find:
The property that Rahal use to rewrite the expression.
Solution:
According to the associative property of addition, if a, b and c are three real numbers, then
[tex]a+(b+c)=(a+b)+c[/tex]
We have,
[tex]-3+[(-7)+(-6)][/tex]
Using the associative property of addition, we get
[tex]-3+[(-7)+(-6)]=[(-3)+(-7)]+(-6)[/tex]
Therefore, the required property is associative property of addition.
what transformation rule represents (-x,-y)
Answers
Answer:
Reflection across the x-axis.
PLEASE HELP QUICK ITS TIMED!!
Which statement correctly describes the data shown in the scatter plot?
A: the point (16,4) is an outlier
B: the scatter plot shows a negative association
C: the scatter plot shows no association
D: the scatter plot shows a nonlinear association
Answers
Answer:
b
Step-by-step explanation:
ANSWER:
It should be B but could be wrong
The perimeter of a triangle is 63m. Two of the sides are 20cm and 27cm. What is the length of the third side.
Answers
Answer:
16cm
Step-by-step explanation:
63 = 20 + 27 + x