Answers
In this case, the equation is in vertex form. To graph the parabola, we need to determine the y-intercept, x-intercept(s), and the vertex.
Vertex of Parabola:Vertex form: y = a(x + h)² - k
⇒ [y = 3(x + 2)² - 1] and [y = a(x - h)² - k] ⇒ Vertex: (h, k) ⇒ (-2, -1)X-intercept(s) of Parabola:Assume "y" as 0.
[tex]\implies 0 = 3(x + 2)^{2} - 1[/tex]
[tex]\implies 1 = 3(x + 2)^{2}[/tex]
Take square root both sides and simplify:
[tex]\implies\sqrt{1} = \sqrt{3(x + 2)^{2}}[/tex]
[tex]\implies1 = \sqrt{3 \times (x + 2) \times (x + 2)}[/tex]
[tex]\implies1 = (x + 2) \times \sqrt{3[/tex]
Divide √3 both sides:
[tex]\implies \±\huge\text{(}\dfrac{1 }{\sqrt{3}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{1} }{\sqrt{3}} \huge\text{)} = (x + 2)[/tex]
Multiply √3 to the numerator and the denominator:
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{1} \times \sqrt{3} }{\sqrt{3\times \sqrt{3}}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} = (x + 2)[/tex]
[tex]\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} - 2 =x[/tex]
[tex]\implies x = \underline{-2.6...} \ \text{and} \ \underline{-1.4...} \ \ \ \ (\text{Nearest tenth})[/tex]
Y-intercept of Parabola:Assume "x" as 0.
⇒ y = 3(0 + 2)² - 1⇒ y = 3(2)² - 1⇒ y = 3(4) - 1⇒ y = 12 - 1⇒ y = 11y-intercept = 11 ⇒ (0, 11)
Determining the direction of the parabola:Since the first cooeficient is positive (+3), the direction of the parabola will be upwards.
Determining the axis of symmetry line:Axis of symmetry line: x-coordinate of vertex
Axis of symmetry line: x = -2
Plot the following on the graph:
y-intercept ---> 11 -----> (0, 11)x-intercept(s) -----> -1.4 and -2.6 -------> (-1.4, 0) and (-2.6, 0)Vertex -------> (-2, -1)Axis of symmetry ----> x = -2Refer to graph attached.
Answer:
VertexVertex form of a quadratic equation:
[tex]y=a(x-h)^2+k\quad \textsf{where }(h,k)\:\textsf{is the vertex}[/tex]
Given equation: [tex]y=3(x+2)^2-1[/tex]
Therefore, the vertex is (-2, -1)
x-intercepts (zeros)The x-intercepts are when [tex]y=0[/tex]:
[tex]\implies 3(x+2)^2-1=0[/tex]
[tex]\implies 3(x+2)^2=1[/tex]
[tex]\implies (x+2)^2=\dfrac13[/tex]
[tex]\implies x+2=\pm\sqrt{\dfrac13}[/tex]
[tex]\implies x+2=\pm\dfrac{\sqrt{3}}{3}[/tex]
[tex]\implies x=-2\pm\dfrac{\sqrt{3}}{3}[/tex]
[tex]\implies x=\dfrac{-6\pm\sqrt{3}}{3}[/tex]
Therefore, the x-intercepts are at -2.6 and -1.4 (nearest tenth)
y-interceptThe y-intercept is when [tex]x=0[/tex]:
[tex]\implies 3(0+2)^2-1=11[/tex]
So the y-intercept is at (0, 11)
Plot the graphAs the leading coefficient is positive, the parabola will open upwards.Plot the vertex at (-2, -1)Plot the x-intercepts (-2.6, 0) and (-1.4, 0)Plot the y-intercept (0, 11)The axis of symmetry is the x-value of the vertex. Therefore, the parabola is symmetrical about x = -2
**You don't need to plot the axis of symmetry - I have added it so that it is easier to draw the curve**
Related Questions
Which of the following sets of data does NOT represent a function?
Set A
X
y
|3
6
s
14
15
9
7
2.
Set B
X
JO
11
y
3
18
2
18
|-7
13
Set C
Answers
The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30
pages, what can you conclude?
O A. About 60% of the books have fewer than
150 pages.
O B. About 16% of the books have fewer than 150 pages.
O c. About 95% of the books have more than 150 pages.
O D. About 16% of the books have more than 150 pages.
Reset
Next
Answers
Answer:
I'm guessing that the answer is OB
Will give Brainliest
At one time, the 1995-1996 chicago bulls had the best record in the history of the NBA, with 72 wins and 10 losses. What percent of their total game did they win?
Please don't solve it but please explaint how to solve it
Answers
Answer:
Step-by-step explanation:
1. Find the total number of games (72 + 10).
2. Find the ratio of wins (72) to this total number (82)
3. Multiply the resulting fraction by 100%
(20 POINTS AND BRAINLIEST) What is the area of the shaded region?
Type only the numeric answer
Answers
Answer:
59 square inches.
Step-by-step explanation:
Equation for area of whole, large triangle:
A = 1/2(b)(h)
A = 1/2(13)(14)
A = 91 square inches
Equation for area of tiny, white triangle:
A = 1/2(b)(h)
A = 1/2(8)(8)
A = 32 square inches
Equation to find the area of the shaded region:
A = 91 - 32
A = 59 square inches
Answer:
64
Step-by-step explanation:
It's 64 because the area is the inside and 8 x 8 = 64.
Can someone please help me with this question?
Answers
Answer:
[tex]\frac{2x}{x+5}[/tex]
Step-by-step explanation:
We are given a function for f and g, and are asked to find f/g.
We know f = 4x^2 + 6x and g = 2x^2 + 13x + 15
Simply put function of f over g.
[tex]\frac{4x^2+6x}{2x^2+13x+15}[/tex]
Factor:
[tex]\frac{2x(2x+3)}{(2x+3)(x+5)}[/tex]
Since both numerator and denominator have 2x + 3, we can cancel them out.
[tex]\frac{2x}{x+5}[/tex] is our answer.
Please help me answer this question!
Answers
Answer:
Step-by-step explanation:
the change in students is 7
The change in textbooks is 35
the consent change is 7:35
Please help with this never good at it
Answers
Answer:
396
Step-by-step explanation:
Divide 3168 by 8 and your answer is 396.
Explain how you can know whether a system of linear equations will have infinite solutions.
Answers
Answer
If the y-intercept and slope of two lines are the same, they are on the same precise line. To put it another way, if the two lines are the same line, the system should have an endless number of solutions.
trust me
Nina signs an)
for her new apartment for a one-year term at $800 a month rent
Answers
Answer:
she would pay 9,600 for 12 months
Step-by-step explanation:
12x800=9,600
Solve this problem:
2x-6=-3(5-x)
Answers
Answer:
x = 9
Step-by-step explanation:
You need to use PEDMAS (Parentheses, exponents, division, multiplication, addition, subtraction) to solve the equation.
1.) Begin by multiplying the values inside of the parentheses by the (-3).
2.) Isolate the variable by adding (15) to both sides.
2.) Isolate the variable by subtracting (2x) from both sides.
Starting Equation.) 2x - 6 = -3(5-x)
1.) 2x- 6 = -15 + 3x
2.) 2x + 9 = 3x
3.) 9 = x
Help. Please!!! 30 points
Answers
B
C
Those three are the answer
Find the median, first quartile, third quartile, and interquartile range of the data.
40,33,37,54,41,34,27,39,35
??????? I haven't heard this before
Answers
Answer:
Median: 37
First quartile: 33.5
Third quartile: 40.5
Interquartile range: 7
Step-by-step explanation:
Your first step should be putting them in order from least to greatest.
27, 33, 34, 35, 37, 39, 40, 41, and 54. Now to find the median you have to find the middle which in the case would be 37. Now to find the 1st quartile u eliminate the meduan and focus on the lower half of the numbers which would be 27, 33, 34, and 35. If you numbers are even you add and divide by 2. In this case you have to add 34 and 33 and then divide by 2 since they are both in the middle. Your 1st quartile would be 33.5. To find the 3rd quartile you do the same thing as the 1st quartile. Only focus on the upper half now. add both the middles then divide by 2 since there are 2 middles. You 3rd quartile should be 40.5. To fine the inerquartile range you subtract the 1st quartile from the 3rd. so it would be 40.5-33.5 which would give you 7. If you want to fine just the range you would subtract the highest number from the lowest number.
What is 3.2×103 in standard form?
Answers
Answer:3200
Step-by-step explanation:
Maliki is building a ramp that is next to a building. The ramp is 5 feet long and has a vertical height of 2 feet. Approximately far away from the building is the ramp? building 2 feet 5 feet
and it is pythagorean theorem
Answers
Answer:
about 4.58 feet
Step-by-step explanation:
[tex] {2}^{2} + {x}^{2} = {5}^{2} [/tex]
[tex]4 + {x}^{2} = 25[/tex]
[tex] {x}^{2} = 21[/tex]
[tex]x = 4.58[/tex]
What is the probability that the sequence is guessed on the first try? startfraction 1 over 24 endfraction one-eighth one-fourth one-third
Answers
The probability that the sequence is guessed on the first try is 1/24
How to determine the probability?The given parameters are:
Colors = 4
Selection = 3
The first color can be selected from any of the 4, the second can be selected from any of the remaining 3 and the third can be selected from any of the remaining 2.
So, the number of sequence is:
Sequence = 4 * 3 * 2
This gives
Sequence = 24
Only one of these sequence is correct
Hence, the probability that the sequence is guessed on the first try is 1/24
Read more about probability at:
https://brainly.com/question/251701
1. What is the degree of 3x³y²z + 2xy³ - 9y + 5?
A. 3
B. 4
C. 5
D. 6
Answers
Answer:
--------------HeyA BenjamiN-----------------
Explanation :
All you need to do is count up the powers of each term and then sum it , the highest power is considered to be the degree.SolvinG :
3x³y²z = 62xy³ = 49y = 1- Our final answer is 6 .
---------------HappY LearninG <3 -------------
Answer:
d. 6
Step by step explanation:
PLEASE HELP!! 7.9 divided by 276.5. Show your work on a paper or online thanks! <3
Answers
Answer:3.5
Step-by-step explanation: Check file
PLS HELP ME?!?!?!
Calculate the area of the following.
Answers
Answer:
678
Step-by-step explanation:
Im pretty sure, but take a look at my work below and see if you think its right:
Find the diameter of the circle with the given circumference. Use 3.14 for pi . C=18 cm
Answers
Answer:
[tex]d=\frac{18}{\pi }[/tex]
Step-by-step explanation:
We work our way backward to find the diameter.
Circumference of a Circle Formula:
[tex]C=2\pi r[/tex]
r is radius , 2*radius = diameter.
Given information: C=18 cm , pi=3.14.
[tex]C=2\pi r\\18=2\pi r\\[/tex]
Get r by itself.
[tex]r=18/2\pi\\r=9/\pi[/tex]
r≈2.864788976
2*r=d
[tex]2*9/\pi =diameter\\d=\frac{18}{\pi }[/tex]
You estimated that you would need 252 more points to move up a level on your favorite video game. But after earning just 240more points, you leveled up! What was your percent error?
Answers
Answer:
5%
Step-by-step explanation:
(240-252/240)×100
Mary and Jim are trying to compare the widths of a window and door. In order to do so, they use strings to measure the widths. They then compare the string lengths to see which one is wider. This is an example of which type of comparison
Answers
Answer:
This is an example of comparing two objects indirectly.
Step-by-step explanation:
whats the numerator for the following rational expression u/v + 2/v =?/v
Answers
Same Denominator We Add The Numerators:
Answer:
[tex]u + 2[/tex]
Need help ASAP! TYSM! Simplify 4√6/√30. Show steps.
Answers
Answer:
Simplify the radical by breaking the radicand up into a product of known factors.
answer
4√5/5
i hope u understand what i meant by that
sry hope this helps
Answer:
4√5/5
Step-by-step explanation:
yw :)
6 Jose burns an average of 200 calories in 25 minutes of running.
Part A
How many calories does Jose burn per minute?
Show your work.
Jose burns
calories per minute.
Answers
Answer:
8
Step-by-step explanation:
200 calories÷25=8
8 calories are burn in a minute.
To check if you answer is right,
8x25=200(8= the calories that are burn in a minute
(25= the full minute)
So Jose burn 8 calories per minute.
Question 2 (5 points)
(03.03, 03.06 MC)
What is the equation of the line that passes through the points (-2, 3) and (2, 7)? (5 points)
оа
x-y=-1
Ob
X-y=-2
Ос
x - y = -5
Od
X-y= -6
Answers
Answer:
[tex]x - y + 5 = 0[/tex]
Step-by-step explanation:
Given:
Line passes through (-2,3) and (2,7)Required:
Find the equation of the lineThe equation of the line passing through two points is given by
[tex]\frac{y-y_{1} }{y_{2}- y_{1} } =\frac{x_{}- x_{1} }{x_{2} -x_{1} }[/tex]
So, [tex]\frac{y-3}{7-3} =\frac{x-(-2))}{2-(-2)}[/tex]
[tex]\frac{y-3}{4} =\frac{x+2}{2+2}[/tex]
[tex]\frac{y-3}{4} =\frac{x+2}{4}[/tex]
Now, [tex]y-3 = x+2[/tex]
On rearranging,
[tex]x - y + 3 + 2 = 0x - y + 5 = 0[/tex]
Therefore, the equation of the line is [tex]x - y + 5 = 0.[/tex]
Anyone one know #14???
Answers
Answer:
d
Step-by-step explanation:
d is the one with both a y squared and x squared making it an ellipse or oval
If x =3+2 root 2 find x - 1/x
Answers
Answer:
-2+2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Since we have the value of x, 3+2[tex]\sqrt{2}[/tex], we can plug that value into the new equation.
We would recieve (3+2[tex]\sqrt{2}[/tex]-1)/3+2[tex]\sqrt{2}[/tex]
Which could simplify to -2+2[tex]\sqrt{2}[/tex]
[tex]x-\dfrac 1x\\\\\\=3+2\sqrt 2- \dfrac 1{3+2\sqrt 2}\\\\\\=3+2\sqrt 2 - \dfrac{3-2\sqrt2}{\left(3+2\sqrt 2\right) \left(3-2\sqrt 2 \right)}\\\\\\=3+2\sqrt 2 -\dfrac{3-2\sqrt 2}{3^2 - \left(2\sqrt 2 \right)^2}\\ \\\\=3+2\sqrt 2-\dfrac{3-2\sqrt2}{9-8}\\\\\\=3+2\sqrt 2-3+2\sqrt 2\\\\\\=4\sqrt2[/tex]
Please help convert this from quadratic form to vertex form
Please show all steps thank you so much!!!
Answers
[tex]y=3x^2+12x+11[/tex]
Step-by-step explanation:To convert this equation into standard form simply expand the equation out using PEMDAS.
PEMDAS
To solve this question you must remember the order of PEMDAS
1) Parentheses
2) Exponents
3) Multiplication and Division
4) Addition and Subtraction
Expanding the Equation
Expand the binomial by raising (x+2) to the second power.
[tex]y=3(x^2+4x+4)-1[/tex]Next, using the distributive property, distribute the 3.
[tex]y=3x^2+12x+12-1[/tex]Then, combine like terms.
[tex]y=3x^2+12x+11[/tex]The length of a rectangle is three times it’s width if the perimeter of the rectangle is 80m find it’s area
Answers
Answer:
=3y^2
Step-by-step explanation:
let,
length: x
width: y
According to condition,
x = 3y -----------(1)
Second condition
Perimeter = 2 (l + b)
80 = 2 (x + y)
x + y = 40 -------------(2)
To find area,
Area = L x B
=3y x y
= 3y^2
Ben works at the Sudsy Scrubbers car wash. Last week, he recorded the number of cars he washed each day.
Answers
Answer:
6 , 25 ,Range
Step-by-step explanation:
Option c is the right answer
I hope it helped you