What is the equation of the following graph in vertex form? parabolic function going down from the left through the point negative four comma zero and turning at the point negative three comma negative one and going up through the point negative two comma zero and then through the point zero comma eight and continuing up towards infinity
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(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where
(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex
This is also called vertex form because the vertex (h,k) is grouped according to their variable.
Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.
The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1
Related Questions
What is the range of y=sec x
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y≤-1, y≥1 is the range of y=sec x
The values where cos(x) is equal to 0 are excluded from the domain of the function y=sec(x)=1cos(x), or the values 2+n for all integers n. The function's range is either y<=1 or y>=1.
What is domain?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
here, we have,
we know that "secant function" mean:
Its root is the Latin verb secare, which means "to cut." Any line that intersects a circle twice is referred to as a secant line, and you can conceive of this line as slicing the circle in half. The distance from the origin to the point where the tangent line intersects the x-axis is the secant function.
now, the identity of the sec is:
1/cos(x) = sec(x) Cot (x) = 1/Tan (x)
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The equation x = 6 represents a vertical line. True or false
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If c1 and c2 are real numbers, give the relationship between them that will allow you to find solutions for the equation x^n + c1 = c2, regardless of the value of n.
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minus c1 from both sides
x^n=c2-c1
take the nth root of both sides
[tex]x=\sqrt[n]{c_2-c_1}[/tex]
dunno about the relationship between them but that's what x is
What is the value of x in this equation: 4x + 5 = 3x + 4? Solve the equation using the algebra tiles. x =
Answers
Answer:
Solution of the equation 4x + 5 = 3x + 4 is:
x= -1
Step-by-step explanation:
We are given a equation:
4x + 5 = 3x + 4
We have to solve the equation for x
4x+5=3x+4
subtracting both sides by 4
4x+5-4=3x+4-4
4x+1=3x
subtracting both sides by 4x
4x|+1-4x=3x-4x
1= -x
⇒ x= -1
Hence, solution of the equation 4x + 5 = 3x + 4 is:
x= -1
Write a word phrase for the algebraic expression 3x+10
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Jenny wants to park in an airport parking lot. The parking lot costs x amount of money per hour, plus an additional parking fee of $10. Jenny stays in the parking lot for 3 hours.
This causes our equation to be 3x (3 hours) + 10 (additional parking fee).
I hope this helps!
when multiplying two or more fractions, you should?
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Last year, Raul estimated that he would need 480 night lights, but he sold 420 night lights. This year, he bought 425 night lights and only sold 375. Which set of statements about the percent errors for the two years is true
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Hope it helped <3
Answer:
The answer is C in edg.
For his craft project, James bought 10 pieces of ribbon that were each 2.1 feet long. How many total yards of ribbon did James buy?
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There is 1 yard in 3 feet. Divide by 3 to convert.
21 / 3 = 7
Therefore he brought 7 yards of ribbon.
James buy 7 yard of ribbon
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
James= 10 pieces of ribbon
Each of length= 2.1 feet
So, length of 10 ribbons
=2.1*10
=21 feet
Now, 1 yard= 3 feet
So, 21 feet= 21/3= 7 yard
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PLZZZ HELP WILL GIVE BRAINLIESTTTT
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Evan bought 6 batteries that cost $10 each and 6 there is that cost $4 each. The total cost was the same as he would have spent buying 6 there is that cost $14 each. So, (6x10)+(6x4). What property does the equation illustrate.
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Nancy rides her bicycle 10 miles at an average rate of 12 miles per hour and 12 miles at an average rate of 10 miles per hour. What is the average rate for the entire trip? Explain your answer.
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1+1=2
Anna paid $4 for renting a video game for 4 days. Which graph shows the relationship between the costs of renting a video game for different days? A graph is shown with title Video Game Rentals. The horizontal axis label is Days, and the vertical axis label is Cost of Rental in dollars.A: Points are plotted on the ordered pairs 2, 1 and 3, 2, and 4, 3. A graph is shown with title Video Game Rentals. The horizontal axis label is Days, and the vertical axis label is Cost of Rental in dollars.B: Points are plotted on the ordered pairs 1, 1 and 2, 2, and 3, 3. A graph is shown with title Video Game Rentals. The horizontal axis label is Days, and the vertical axis label is Cost of Rental in dollars. C:Points are plotted on the ordered pairs 1, 2 and 2, 3, and 3, 4. A graph is shown with title Video Game Rentals. The horizontal axis label is Days, and the vertical axis label is Cost of Rental in dollars.D: Points are plotted on the ordered pairs 0, 0 and 1, 4, and 1.5, 6.
Answers
A horizontal axis is labeled days, a vertical axis is labeled cost of rental.
(x,y)...x is gonna be ur days and y is gonna be ur cost of rental
ur equation is gonna be y = x
points are plotted (1,1) , (2,2), (3,3)
^^ this is the graph u use ...graph B
Yasir designs bracelets. He uses between 9 and 15 red and yellow beads in a ratio of 2 red beads to 5 yellow beads. Drag the beads into the box to meet these requirements.
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2+5=7 is less that the total number of beads per bracelet.
so we multiply both (2 and 5) by 2, and get (4 and 10) red beads and yellow beads.
4+10=14, so the total number is between 9 and 15 as required.
Answer:
4 red beads
10 yellow beads
Answer:
You should place 4 red beads and 10 yellow beads into the container
Step-by-step explanation:
Write an algebraic expression for 15 decreased by twice a number
Answers
15-2x
Hope this helps!
-Benjamin
Jared flipped a fair coin 50 times. He expected half of his tosses to land on heads, but he only got heads 15 times. If he increased the number of times he flipped the coin to 500, he should expect the number of heads to be-
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how many solutions does the equation 4y+7=5+2+4y have?
A. one
B. two
C. None
D. infinitely many
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4y + 7 = 7 + 4y
same line....infinite solutions
A store had 235 MP3 players in the month of January. Every month ,30% of the MP3 players were sold and 50 new MP3 players were stocked in the store. Witch recursive best represents the number of MP3 players in the store f(n) after n months?
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What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4?
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To solve this problem, we are given the formulas for our new x and y. To use this formula, we must first establish our points 1 and 2. Since the problem specifically directed the point E which partitions the line segment “from J to K”, therefore
point 1 = point J = (x1, y1)
point 2 = point K = (x2, y2)
The variables m and n indicates the portion of partition segment JE and EK that takes up from the original segment. Since the ratio is 1:4, then:
JE = m = 1
EK = n = 4
Therefore calculating for x and y using the given formulas:
x = [1 / (1 + 4)] (25 – (-15)) + (-15)
x = -7
y = [1 / (1 + 4)] (15 – (-5)) + (-5)
y = -1
Therefore the coordinates of point E is (-7, -1)
The x- and y- coordinates of point E (-7,-1)
Further explanationIn the coordinates of the two-dimensional plane (xy) there is a position vector.
Two dimensions because the coordinates are only x and y, three dimensions if the coordinates are x, y, and z.
If there is a point P then
You can write P as:
P = xi + yi
where i denotes the unit vector in the x and y directions
While the size of the vector:
[tex]\displaystyle P = \sqrt{x^2+y^2}[/tex]
and its direction
[tex]\displaystyle \theta=arc\:tan\:\frac{y}{x}[/tex]
If a point C divides the line segment AB by the ratio m: n, then the coordinates of point C can be formulated:
[tex]\displaystyle \vec{C}=\frac{m\vec{b}+n\vec{a}}{m+n}[/tex]
Coordinate x :
[tex]\displaystyle x=\frac{m.x_2+n.x_1}{m+n}[/tex]
Coordinate y :
[tex]\displaystyle y=\frac{m.y_2+n.y_1}{m+n}[/tex]
line segment from J to K into a ratio of 1:4, then m = 1 and n = 4
(x1,y1) from point J= (-15,-5)
(x2,y2) from point K= (25,15)
So coordinates of point E :
Coordinate x :
[tex]\displaystyle x=\frac{1.25+4.-15}{5}[/tex]
x = -7
Coordinate y :
[tex]\displaystyle y=\frac{1.15+4.-5}{5}[/tex]
y = -1
Learn more
Which vector should be negative
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the statements that describe a vector
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the resultant vector
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Keywords: line segment, vector, two-dimensional coordinates , x,y, partitions
What's the area of a circle with a radius of 5?
Answers
given that the radius=5 units
area=pi 5²=25pi
area=25pi square units
if we use pi=3.14 aprox then
area=78.5 square units
To take a taxi, it costs $3 plus an additional $2.00 per mile traveled. You spent exactly $ 20 on a taxi, which includes the $1 tip you left. How many miles did you travel
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19=3+2x
16=2x
x=8
Answer: 8 miles
find the solution of the system of equations 2x-4y=32 2x-8y=48
Answers
2x-8y=48
--------------subtract
4y = - 16
y = -4
2x-4y=32
2x- 4(-4)=32
2x + 16 = 32
2x = 16
x = 8
answer
(8, -4)
2x - 8y = 48
Multiple equation 2 by -1 so the 'x' variables will cancel.
-1(2x - 4y = 32)
-2x + 4y = - 32
2x - 8y = 48
-------------------- add
- 4y = 16 divide both sides by -4
y = -4
Plug -4 back into either equation and solve for y.
2x - 4y = 32
2x -4(-4) = 32
2x + 16 = 32 subtract 16 from both sides
2x = 16 divide both sides by 2
x = 8
(8, -4)
What value does 4 represent in the number 487.009
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find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. Use pi=3.14 when necessary. cylinder with these 6ft, 18ft, 30 ft.
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The volume of any cylinder is the area of the top circle (pi×r^2) times the height (h) of the cylinder, where r=radius of the circle. So: h×pi×r^2
The heights are the same for C and c, so we can call that h in both, which = 30ft. Now C's radius (R) = 1/2 of diameter, which is 18ft. So R = 9ft
c's radius (r) is 1/2 of its diameter, which is 6ft. So r = 3ft. Now we can set it up:
C - c = (h×pi×R^2) - (h×pi×r^2)
*since the h and pi in both formulae are multiplied by the other variable, we can factor that out:
h×pi(R^2) - h×pi(r^2) = h×pi(R^2-r^2)
h×pi = 30ft.×3.14 = 94.2ft. -->
94.2ft(9ft^2-3ft^2) = 94.2ft(81-9ft^2)
= 94.2ft(72ft^2) = 6782.4 ft.^3
A student wants to report on the number of movies her friends watch each week. The collected data are below:
2
14
1
2
0
1
0
2
Which measure of center is most appropriate for this situation and what is its value?
Median, 1.5
Median; 3
Mean, 1.5
Mean; 3
Answers
Answer:
A) Median, 1.5
Step-by-step explanation:
Since we have given that the collected data as follows:
| 2 | 14 | 1 | 2 | 0 | 1 | 0 | 2 |
As we know that there are three measures of central tendency.
1) Mean is given by
2) Media of 0, 0, 1, 1, 2, 2, 2, 14 is given by
3) Mode of 0,0,1,1,2,2,2,14 = 2as 2 is occurring most of the times, but we know that median is the best measure to find the center. Hence, Median is the best measure and its value is 1.5.
A triangle has one side that measures x, and the other two sides each measure 4 inches less than x. The perimeter is 19 inches.
What is the measure of x?
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x + (x - 4) + (x - 4) = 19
3x - 8 = 19
3x = 19 + 8
3x = 27
x = 27/3
x = 9 <==
Answer: Simplified version of the answer above: (x = 9) is the correct answer.
Step-by-step explanation:
the age of two groups of yoga students are shown in the following dot plot
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The answer is choice A.
Which expression shows a sum of three terms?
3x
3 + x
x3
x + 3 + x
Answers
x + 3 + x <==
___________________________________________________
The three (3) terms are: "x" , "3" , and "x" .
___________________________________________________
Answer choice [A]: "3x" ; only has one term.
___________________________________________________
Answer choice [B]: "x + 3 " ; only has two terms: "x" and "3" .
___________________________________________________
Answer choice [C]: "x³ " ; only has one term.
___________________________________________________
Find the sum of this infinite geometric series where a1=0.3 and r=0.55
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We know that in a geometric sequence defined by [tex]\mathsf{a_1}[/tex] and [tex]\mathsf{r}[/tex] , the sum can be calculated the following way:
[tex]\mathsf{S_n = \dfrac{a_1}{1-r}}\\ \\ \\ \\ \mathsf{S_n = \dfrac{0.3}{1-0.55}}\\ \\ \\ \mathsf{S_n = \dfrac{0.3}{0.45}}\\ \\ \\ \boxed{\mathsf{S_n = \dfrac{2}{3}=0.666...}}[/tex]
Answer:
The sum of the infinite geometric sequence is given by:
[tex]S_{\infty} = \frac{a_1}{1-r}[/tex] ....[1]
where,
[tex]a_1[/tex] is the first term
r is the common ratio.
As per the statement:
Given that [tex]a_1 = 0.3[/tex] and r = 0.55
To find the sum of this infinite geometric series.
Substitute the given values in [1] we have;
[tex]S_{\infty} = \frac{0.3}{1-0.55}[/tex]
⇒[tex]S_{\infty} = \frac{0.3}{0.45}[/tex]
Simplify:
[tex]S_{\infty} \approx 0.67[/tex]
Therefore, the sum of this infinite geometric series approximate is, 0.67
Simplify (−34.67)0.
−34.67
−1
0
1
Answers
Answer:
The answer is 1.
Im sorry I forgot the step by step explanation, but I had this in a quuiz a while ago and the answer is 1.
What is the equation of the line of reflection in the following coordinate plane?
x = 0
y = 2
x = 1
y = 1
Answers
Answer:
x = 1
Step-by-step explanation: