The required time to travel 30 miles is given as 45 minutes and 3/4 hours.
Given that,
A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Speed = Distance/time
Speed = 20 / [1/2]
Speed = 40 miles per hour,
Time = Distance / Speed
Time = 30 / 40
Time = 3 / 4 hour
Thus, the required time to travel 30 miles is given as 45 minutes and 3/4 hours.
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in each of the following cases, you are given a set of numbers. in each case, determine whether this set of numbers can be a domain of convergence for a power series. if it cannot, explain why it cannot. if it can, give an example of a power series that has this set as its domain of convergence.
a. [-1,3)
b. (-1,3)
c. (-1,3]
d. [-1,3]
The possible domain of the convergence are b. (-1,3) and c. (-1,3]
Domain of convergence.
In statistics, domain of the convergence also known as interval of convergence means an interval associated with a given power series such that the series converges for all values of the variable inside the interval and diverges for all values outside it.
Given,
Here we need to identify in which of the options are domain of convergence.
As per the definition of domain of convergence, the interval of the convergence is (-∞ , ∞).
So, the possible convergence in the given options are (b) and (c).
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Ball A is dropped from the top of a building. At the same instant, ball B is thrown vertically upwards from the ground. When the balls collide, they are moving in opposite directions and the speed of A is twice the speed of B. At what fraction of the height of the building did the collision occurs? B. 2/3
The fraction of height at which the collision occured is , y/y₀ = 1/2 + v₀²/(2 g y₀) .
For ball A
Given that the ball is dropped and its initial velocity is zero, the equation is
= - 2 g (y₀-y)
For ball B
v {B}^2 = v₀² - 2 g y
We swap out
2v {B}^2 = -2 g (y₀ -y)
g y0 + 2 g y = -v B2
v {B}^2 = v₀² - 2gy
It can be solved because it is a system of two equations with two unknowns. Let's add and multiply by -1.
0 = g y₀ + v₀² -2gy
Bypassing the height
y = (g yo plus v02) / 2g
y = yo / 2 + v₀² / 2g
In this exercise, we'll assume that the building's height and ball B's initial velocity are both known.
The percentage is
y/yo
= 1/2 + v₀²/(2gyo) (2gyo)
Velocity and speed describe how quickly or slowly an object is moving. We frequently encounter circumstances when we must determine which of two or more moving objects is going faster.
If the two are travelling on the same route in the same direction, it is simple to determine which is quicker.
It is challenging to identify who is moving the fastest when their motion is in the other direction.
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Question Answer Equation Joan found 70 seashells on ...
The number of seashells that Joan gave to Sam is 43 .
In the question ,
it is given that ,
the total number of seashell that Joan found on the beach is = 70 ,
let the number of seashells that she gave to Sam be "x" .
the number of seashells that Joan has with her is = 27 .
So , the equation that represents the above situation about the number of seashells is
27 + x = 70
subtracting 27 from both sides of the equation ,
x = 70 - 27
Simplifying further ,
we get ,
x = 43
Therefore , the number of seashells given is 43 .
The given question is incomplete , the complete question is
Joan found 70 seashells on the beach . she gave Sam some of her seashells . She has 27 seashell . How many seashells did she give to Sam ?
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A translation is applied to the triangle formed by the points A(−1, 4) , B(−1, 10) , and C(3, 6) . The image is the triangle that has vertices A′(3, 4) , B′(3, 10) , and C′(7, 6) . Select the phrase from the drop-down menu to correctly describe the translation.
Answer:
The triangle was translated to the right by 4 points.
Step-by-step explanation:
If you look at the coordinates, the Y value does not change at all when comparing the original image to the translated image. Only the x value was translated. Since the problem told you it was a translation you can pick a point and subtract the value of the original image from the value of the translated image. If your answer to the subtraction problem is positive, the image moved to up or to the right (for the x-axis), if it is negative then your image moved down or to the left . Up and down is for translations along the Y-axis, and left and right are for translations along the X-axis. This works for both X and Y values. I know I just dumped a bunch of words on you, so to show you lets use points C and C'. C has an X value is 3 and C' has an X value of 7.
Subtract C (3) from C' (7) and that'll give you an answer of 4. Since the answer is positive it will move up or to the right. Since we used the X value, it moved to the right.
If you need a better explanation let me know and I'll try my best.
A grocery store wonders if their sales will be better if they play ambient music or no music at all. Each day for 2 months, the manager flips a coin to determine whether or not the store will play music that day. At the end of the 2 months, the manager finds that, on average, sales were significantly better on days where music was playing. Is this an experiment or an observational study?
Answer:
It is a observational study
Step-by-step explanation:
in the expression 7a + b-12 which is a constant
Answer: Its -12
Step-by-step explanation:
In Algebra, a constant is a number on its own.
What is the angle measurement and angle relationship?
An angle is formed when two lines or rays meet at a common point. The common point is known as the vertex.
An angle measurement can be defined as the measure of the angle formed by the two rays or arms at a common vertex. Angles are measures in degrees. There are many kinds of angles in geometry such as acute, obtuse, reflex, straight and right angle. Each angle has a different measure.
Angle relationship between the angles made when a line intersects a pair of parallel lines.
In geometry, there are five fundamental angle pair relationships such as complementary angles, supplementary angles, adjacent angles, linear pair, vertical angles.
The more familier unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°. Two angles are complementary if the sum of their measures is 90°.
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Show that the solution of the Neumann problem vều = 0 if r < R, un(R, ) = f(0) (where UN du/aN is the directional derivative in the direction of the outer normal) is u(r, 6) = Ao + r™(An cos nd + Bn sin në) B) n=1 with arbitrary Ao and 1 An focos no do, TORN-1 -TT 1 Bn = fe sin no do. TTnR7 -1 -TT
The solution of Neumann problem, ∇²u= 0 if r < R , Uₙ (R,θ) = f(θ) is u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ) with boundary conditions uᵣ (r,θ) = ∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ) and
Aₙ=∫(f(θ)cosnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]
Bₙ=∫(f(θ)sinnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]
Given that
The solution of Numann problem
∇²u= 0 if r < R , Uₙ (R,θ) = f(θ)
Use polar co-ordinates (r,θ)
uᵣᵣ + 1/r uᵣ+ 1/uᵣ (uθθ) = 0 ,0 < r< R,
0 <θ <2π and ∂u/∂r(R,θ) = f(θ) is directional derivative
r²d²u/dr² + rdu/dr + d²u/dθ² = 0
Let , r = ε⁻ᵗ , u(r(t),θ)
uₜ = uᵣ(rₜ) = - e⁻ᵗ uᵣ
uₜₜ =( - e⁻ᵗ uᵣ )ₜ = ε⁻ᵗuᵣ + e⁻²ᵗ uᵣᵣ
= r uᵣ+ r²uᵣᵣ
Thus we have, uₜₜ + uθθ = 0
Let u(t,θ) = X(t)Y(θ)
Which gives X''(t)Y(θ) + X(t)Y"(θ) = 0
X"(t)/X(t) = - Y"(θ)/Y(θ) = λ
From Y"(θ) + λ Y(θ) = 0
We get, Yₙ(θ) = aₙ cosnθ + bₙ sinnθ
λ= n² , n =0, 1, ...
With these values of λn we solve,
X"(t) - n² X(t) = 0
If n = 0 , X₀(t) = c₀t + d₀
X₀(r) = -c₀log (r) + d₀
If n not equal to 0 then
Xₙ (t) = cₙeⁿᵗ + dₙ e⁻ⁿᵗ
Xₙ(r) = cₙ(r)⁻ⁿ + dₙ (r)ⁿ
We have u₀(r, θ) = X₀(r)Y₀(θ)
= a₀ ( - c₀(log r) + d₀)
uₙ(r,θ) = Xₙ(r) Yₙ(θ)
= (cₙ r⁻ⁿ+ dₙrⁿ)(aₙ cosnθ + bₙ sinnθ)
But u must be positive at t =0
So, cₙ = 0 ; n = 0,1,2....
u₀ (r,θ) = a₀ d₀
uₙ(r,θ) = dₙ rⁿ( aₙ connθ + bₙ sinnθ)
By superposition , we can write as
u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ)
Boundary conditions gives
uᵣ (r,θ)=∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ)
the coefficients aₙ , bₙ for n ≥ 1 are determined are Fourier series for f(θ)
but a₀ is not determined from f(θ) therefore , it may take arbitrary value. By using Fourier series,
Aₙ= Integration of(f(θ)cosnθ dθ/π n R⁽ⁿ⁻¹⁾) where θ∈[-π, π]
Bₙ= Integration of (f(θ) sinnθ dθ/π nR⁽ⁿ⁻¹⁾) where θ∈[-π, π]
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How many subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence?
This 90% confidence level requires subjects. (Round up to the nearest subject
Answer:
Step-by-step explanation:
To determine the number of subjects needed to estimate the mean number of books read the previous year within six books with 90% confidence, you would need to use a sample size calculation. There are several factors that can affect the sample size needed, including the desired level of confidence, the desired level of precision, the variability of the population being sampled, and the size of the population.
One way to calculate the sample size is to use a sample size calculator, which can be found online or in statistical software. These calculators typically ask for the desired level of confidence, the desired level of precision, and the estimated standard deviation of the population being sampled.
Alternatively, you can use a sample size formula to calculate the sample size. For example, the formula for calculating the sample size for a simple random sample with a known population standard deviation is:
n = (Z*sigma / E)^2
where n is the sample size, Z is the z-score corresponding to the desired level of confidence (e.g., for a 90% confidence level, Z would be 1.645), sigma is the population standard deviation, and E is the desired level of precision (e.g., 6 books in this case).
To use this formula, you would need to know the population standard deviation, which may require collecting data from a pilot study or using estimates based on similar populations.
It's important to note that sample size calculations are based on statistical assumptions, and the actual sample size needed may vary depending on the specific characteristics of the population being sampled. Additionally, sample size calculations are based on estimates, so the actual level of precision may differ from the desired level.
Shaina is 55 kg.what is Shaina's weight in grams?
Answer:
55000 grams
Step-by-step explanation:
1 kg = 1000 grams ==> kilo means 1000, so 1 kilogram = 1000 grams
Now multiply 55 kg with the grams-kilograms conversion factor to get the total number of grams Shaina weighs.
55 kg* 1000 grams / 1 kg =
55 * 1000 grams / 1 = ==> cancel out the kg
55 * 1000 = 55000 grams
Find the first three nonzero terms in the Taylor polynomial approximation to the DE V" +9y + 5y3 = cos(10t), y(0) = 0, y' (0) = 1.
The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .
In the question ,
it is given that ,
the differential equation is
y'' + 9y + 5y³ = Cos(10t) ...equation(1)
y(0) = 0, y'(0) = 1
for y = 0 , the differential equation is
y''(0) + 9y(0) + 5{y(0)}³ = Cos90)
y''(0) + 9 + 5 = 1 ;
y''(0) = 1.
differentiating equation(1) with respect to "t" , we have
y''' + 9y' + 15y²y' = -10Sin(10t)
y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)
y'''(0) + 9 + 0 = 0
y'''(0) = -9
The Taylor series is given by
y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....
Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have
y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....
= t + t²/2 - 3/2.t³ + ...
Therefore , the first three terms are t , t²/2 , -3/2.t³ .
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A and B are events defined on a sample space, with P(A) = 0.6 and P(BIA) = 0.3. Find P(A and B)
A and B are events defined on a sample space, with P(A) = 0.6 and P(BIA) = 0.3. then P(A and B) = 0.18
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
If A and B are events defined on the sample space with P(A) = 0.6 and P(BIA) = 0.3.
To find P(A and B),
we use the formula of conditional probability,
P( A and B ) = P (BIA) P(A)
P( A and B ) = 0.6 × 0.3
P( A and B ) = 0.18
Therefore, P ( A and B ) is 0.18.
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A baker has 1 1/4 cups of sprinkles, and he buys another 1/2 cup of sprinkles. He plans to use them to spread on cupcakes. Each cupcake needs 1/8 cup of sprinkles. How many cupcakes can the baker sprinkle?
Answer:
i think it 5/
orry if i wrong
Step-by-step explanation:
what’s 12.56981 rounded to nearest hundredth?
Answer:12.57
Step-by-step explanation:
The given decimal rounded to the nearest hundredth would be 12.57.
Hope this helps!
1. Let N be set of New England states {ME, NH, VT, MA, CT, RI }. (See map provided.) (Note that Maine is abbreviated as ME and Massachusetts as MA.) For each of the following parts, either give an example of a relation on the set of New England states N that has the noted properties, or else show that no such relation exists. (a) A relation R on N that is reflexive and symmetric but not transitive. (b) A relation S on N that is reflexive and transitive but not symmetric. (c) A relation T on N that is transitive and symmetric but not reflexive.
A relation R on N that is reflexive and symmetric but not transitive of example is { N , ME , MA } .
Given :
Let N be set of New England states {ME, NH, VT, MA, CT, RI }. (See map provided.) (Note that Maine is abbreviated as ME and Massachusetts as MA.) For each of the following parts, either give an example of a relation on the set of New England states N that has the noted properties, or else show that no such relation exists.
a )
A relation R on N that is reflexive and symmetric but not transitive of example is { N , ME , MA } .
b )
A relation S on N that is reflexive and transitive but not symmetric is { MA , CT , RI } .
c )
A relation T on N that is transitive and symmetric but not reflexive is { ME , NH , VT } .
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From previous studies, it is concluded that 80% of workers indicate that they are satisfied with their job. A researcher claims that the proportion is significantly different than 80% and decides to survey 300 working adults. Test the researcher's claim at the
α=0.02 significance level.
Answer:
To test the researcher's claim, we need to conduct a hypothesis test. The null hypothesis, denoted as H0, is that the proportion of workers who are satisfied with their job is equal to 80%, and the alternative hypothesis, denoted as Ha, is that the proportion is significantly different than 80%.
To conduct the hypothesis test, we first need to calculate the sample proportion of workers who are satisfied with their job. To do this, we need to know how many of the 300 workers surveyed indicate that they are satisfied with their job. Without this information, it is not possible to conduct the hypothesis test.
Step-by-step explanation:
what is the distance from (3 and one-half, 5) to (3 and one-half, โ12)?; lcm of 7 and 9; common multiples of 6 and 8; how to find the lcm; what is lcm in math
The distance between the points (3[tex]\frac{1}{2}[/tex], 5) and ( 3[tex]\frac{1}{2}[/tex], 12) is 7 units
The coordinates of the first point = ( 3[tex]\frac{1}{2}[/tex], 5)
The coordinates of the second point = ( 3[tex]\frac{1}{2}[/tex], 12)
First convert the mixed fraction to simple fraction
3[tex]\frac{1}{2}[/tex] = 7/2
The coordinates of the points will be (7/2, 5) and (7/2, 12)
The distance between the two points = [tex]\sqrt{(x_1-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the values in the equation
= [tex]\sqrt{(\frac{7}{2}-\frac{7}{2})^2+(12-5)^2 }[/tex]
Subtract the numbers
= [tex]\sqrt{0^2 + 7^2}[/tex]
Take sum of the square of the terms and find the square root
= 7 units
Therefore, the distance between the points is 7 units
I have solved the question in general, as the given question is incomplete
The complete question is:
what is the distance from (3 and one-half, 5) to (3 and one-half, 12)?
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Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as the one shown.8x + 7y = 394x - 14y = -68
Answer:
Solution of the given equation by elimination method is x=0.5 and y=5.
Step-by-step explanation:
8x + 7y = 39 --------------(1)
4x - 14y = -68 ------------(2)
Multiply the equation 2 by -2, then add the equations along.
Equation (2) multiply by -2 : -8x +28y = 136
8x + 7y = 39 --------------(1)
-8x +28y = 136-----------(2)
Add these equations to eliminate x:
0x+35y=175
35y=175
y=5
Substitute y=5 in 8x+7y=39:
8x+(7)(5) =39
8x+35=39
8x=39-35
8x=4
X=8/4
x=0.5
Solution of the given equation by elimination method is x=0.5 and y=5.
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How many 2 1/3 m lengths of rope can be cut from a rope of length 21 m?
Which table of values matches the equation y - 3x - 3?
As a result, the second table agrees with the formula y= 3x -3.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
-3x - 3 = -6
y= 3x -3
Therefore, the second table matches the equation y= 3x -3.
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7. After paying $5.00 for a salad, Taylor has no more than $27.00 left. How
much money did she have before buying the salad?
(Set up inequality!)
Answer:
32.00 dollars before she bought the salad
Evaluate 2xx ÷ 3yy for x = 1 2 and y = 3 5 -show the steps
The value of 2xx ÷ 3yy is 288/1225
What is simplification?In mathematics, simply or simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.
Given that, an expression 2xx ÷ 3yy, where x = 12 and y = 35
2x12x12/3x35x35 = 288/1225
Hence, The value of 2xx ÷ 3yy is 288/1225
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Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply: 83, 12.13) points 53, 11.83) points (8.45, 11.51) points (8.63, 11.33) points Cannot be determined with the information given: Saved
The reasonable 95% confidence intervals for the population mean difference is (7.83, 12.13) , the correct option is (a) .
In the question ,
it is given that ,
90% confidence interval is given as (8.21 , 11.75)
using this interval , we have to find the 95% confidence interval .
Now, [tex]x_{d}[/tex] - E = 8.21
[tex]x_{d}[/tex] + E = 11.75 , where E is the margin of Error .
Solving the equations ,
we get ,
E = 1.77 and [tex]x_{d}[/tex] = 9.98
So , the margin of error E is given as
E = [tex]t_{\frac{0.10}{2},15 } \times \frac{S.D.}{\sqrt{n} }[/tex]
we have to find standard deviation from this ;
given n = 16 and [tex]t_{\frac{0.10}{2},15 }[/tex] = 1.7531
Substituting in the margin of error equation ,
we get ,
S.D. = (1.77 × 4)/1.7531
= 4.0386
So , the 95% confidence interval is given as [tex]x_{d}[/tex] ± [tex]t_{\frac{0.10}{2},14 } \times \frac{S.D.}{\sqrt{n} }[/tex] .
from t table , [tex]t_{\frac{0.10}{2},14 }[/tex] = 2.1314
Substituting ,
we get ,
CI = (9.98 ± 2.1314×4.0386/√16)
= (9.98 ± 2.1519)
= ( 9.98 - 2.1519 , 9.98 + 2.1519)
= (7.83 , 12.13)
Therefore , the correct option is (a) (7.83 , 12.13) .
The given question is incomplete , the complete question is
Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply:
(a) (7.83, 12.13)
(b) (7.53, 11.83)
(c) (8.45, 11.51)
(d) (8.63, 11.33)
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Two parallel lines passing the vertices with red line r at points (c, d) at (2, 10) and (0, b) at (0, 6) and blue line s intercepts (c, 0) at (2, 0) and (0, a) at (0, minus 4) Statements Reasons 1. given 2. application of the slope formula 3. distance from to equals the distance from to definition of parallel lines 4. application of the distance formula 5. substitution property of equality 6. inverse property of addition 7. substitution property of equality Which step of the proof contains an error? A. Step 5 B. Step 6 C. Step 2 D. Step 4
Answer:
transitive property
Step-by-step explanation:
Solve for b.
6+b=a pls help
Answer:
b = a - 6
Step-by-step explanation:
Solve for b:
6 + b = a
6 + b - 6 = a - 6
b + 0 = a - 6
b = a - 6
I need help with this please help me
By using the fact that segment DC bisects the angle BCA, we will see that:
m∠DCB = 67.38°
How to find the measure of angle BCD?
First, we know that the angle CDB is an angle of 90°, and the angle ACB has a measure of 134.76°.
Now, notice that the segment DC bisects that angle (bisects means that it "cuts it" right in half), then the angle BCD is half of that, we will have:
∠DCB = 134.76°/2 = 67.38°
In this way we conclude that the measure we wanted to find is 67.38°.
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PLEASE HELP I HAVE GRAPH TOO
A 2010 estimate of Australia's population is
21,515,754.
The next 3 questions ask about this data.
- How many people in Australia
Would be expected to have type
O blood?
We calculated from the graph that 10542719 people expected to have type O blood.
What is different blood group?Generally, human body contains any of these four common types of blood. These are type A, B, O and AB.
How can we estimate our population as per blood group?If we want to estimate our population containing different blood group. we need to carry out survey study to colect data.
Given, Estimated population in 2010 =21515754
the population in percentage who may have O type blood =49%
Actual number of people who expected to have O type blood =
(21515754×49)/100
=10542719
hence, total 10542719 people expected to have O type blood.
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Please help! The answer options for the select button are:
SELECT; SELECT;
-1.025 Percent per decade
-2.5 percent per year
The average rate of change from 1992 to 2000 is -1.025 percent per decade.
What is the average rate of change?
It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
the average rate of change :
A(x) = 34.5 - 42.7 / 2000 - 1992
A(x) = -8.2 / 8
A(x) = -1.025
Hence, the average rate of change from 1992 to 2000 is -1.025 Percent per decade.
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a is an infinitesimally stochastic matrix (i.e., its rows sum to zero). prove that e at is a stochastic matrix.
A stochastic matrix A's steady state is an eigenvector w with eigenvalue 1, such that the elements are positive and add up to 1. The theorem of Perron-Frobenius...
A square matrix A is stochastic if all of its entries are nonnegative, and the elements of each column total to 1. If all of the elements in a matrix are positive integers, the matrix is positive.
A stochastic matrix is a square matrix with probability vector columns. A probability vector is a numerical vector with entries that are real values ranging from 0 to 1 and whose sum equals 1.
(Stochastic processes, mathematics) A square matrix of rows of nonnegative real values, with each row adding up to A Markov chain's transitions are described by its element in the 'th row and 'th column, which describes the probability of moving from state to state in one time step.
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The following graph shows a top-opening parabola.
What is the vertex form of the equation that represents this parabola?
Responses
y=(x−9)2−1y is equal to open paren x minus 9 close paren squared minus 1
y=(x+1)2−9y is equal to open paren x plus 1 close paren squared minus 9
y=(x+9)2−1y is equal to open paren x plus 9 close paren squared minus 1
y=(x−1)2−9
Answer:
(b) y=(x+1)²−9
Step-by-step explanation:
You want the vertex form equation of the graphed parabola, which opens upward and has its vertex at (-1, -9).
Vertex formThe vertex form equation for a parabola with vertex (h, k) is ...
y = (x -h)² +k
The vertex of the parabola shown is (h, k) = (-1, -9). Using these values in the equation gives ...
y = (x +1)² -9
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Additional comment
The equation may include a scale factor that multiplies the square. Here, the curve rises 1 unit for 1 unit either side of the vertex, so the scale factor is 1. (The rise at ±1 from the vertex is the scale factor.)
Steps: (1) read the vertex coordinates from the graph; (2) put those coordinates in the vertex form equation; (3) check to see that the vertical scale factor is 1.
