A box contains green marbles and blue marbles. Yosef shakes the box and chooses a marble at random. He records the​ color, then places the marble back into the box. Yosef repeats the process until he chooses 50 marbles. The table shows the count for each color. Write a probability model for choosing a marble.

green: 36
blue: 14

Answer:

7

Step-by-step explanation:

the range is the difference between the highest and lowest value in a data set.

13 is the highest in the distribution

6 is the lowest in the distribution

13-6=7

Give brainliest, please!

Hope this helps :)

The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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The series ∑ₙ=₁ to ∞ (n/n² + 6) is divergent.

To determine whether the series ∑ₙ=₁ to ∞ (n/n² + 6) is convergent or divergent, we can use the Integral Test.

The Integral Test states that if f(x) is a continuous, positive, and decreasing function on the interval [1, ∞) and f(n) = aₙ for all positive integers n, then the series ∑ₙ=₁ to ∞ aₙ and the integral ∫₁ to ∞ f(x) dx either both converge or both diverge.

In this case, let's consider the function f(x) = x/(x² + 6). We can check if it meets the conditions of the Integral Test.

Positivity: The function f(x) = x/(x² + 6) is positive for all x ≥ 1.

Continuity: The function f(x) = x/(x² + 6) is a rational function and is continuous for all x ≥ 1.

Decreasing: To check if the function is decreasing, we can take the derivative and analyze its sign:

f'(x) = (x² + 6 - x(2x))/(x² + 6)² = (6 - x²)/(x² + 6)²

The derivative is negative for all x ≥ 1, which means that f(x) is a decreasing function on the interval [1, ∞).

Since the function f(x) = x/(x² + 6) satisfies the conditions of the Integral Test, we can evaluate the integral to determine if it converges or diverges:

∫₁ to ∞ x/(x² + 6) dx

To evaluate this integral, we can perform a substitution:

Let u = x² + 6, then du = 2x dx

Substituting these values, we have:

(1/2) ∫₁ to ∞ du/u

Taking the integral:

(1/2) ln|u| evaluated from 1 to ∞

= (1/2) ln|∞| - (1/2) ln|1|

= (1/2) (∞) - (1/2) (0)

= ∞

The integral ∫₁ to ∞ x/(x² + 6) dx diverges since it evaluates to ∞.

According to the Integral Test, since the integral diverges, the series ∑ₙ=₁ to ∞ (n/n² + 6) also diverges.

Therefore, the series ∑ₙ=₁ to ∞ (n/n² + 6) is divergent.

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Incomplete question:

Use the Integral Test to determine whether the series is convergent or divergent.

∑ₙ=₁ to ∞ = n/n² + 6

Evaluate the following integral ∫₁ to ∞ x/x²+6 . dx

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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Answer:

oooo[[oooo seven. my boy o girl

Answer:

-3

Step-by-step explanation:

porque si debes 5 y pagas 2 quedas debiendo 3 sé que no es la mejor explicación pero bueno...

Answer:

  x ≈ 2.467

Step-by-step explanation:

You want the solution to 5^(3x -2) = 7^(x +2).

Logarithms turn an exponential problem into a linear problem. Taking logs, we have ...

  (3x -2)·log(5) = (x +2)·log(7)

  x(3·log(5) -log(7)) = 2(log(7) +log(5)) . . . . . separate variables and constants

  x = log(35²)/log(5³/7) = log(1225)/log(125/7) . . . . divide by x-coefficient

  x ≈ 2.46693

__

Additional comment

A graphing calculator can solve this nicely as the x-intercept of the function f(x) = 5^(3x-2) -7^(x+2). Newton's method iteration is easily performed to refine the solution to calculator precision.

Answer:

idk

Step-by-step explanation:

idk just responding

for points

Answer:

120 miles

Step-by-step explanation:

If 1 inch = 20 miles, you can multiply both sides by 6 to figure out how many miles 6 inches represent.

Answer:

A one tailed test

Step-by-step explanation:

Chi-Square Distributions That Are Positively Skewed Have A Research Hypothesis That Is A One-Tailed Test.

Chi-Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom.

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One-Tailed Test

Chi-Square distributions that are positively skewed have a research hypothesis that is a One-Tailed Test.

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Answer:

7 or any number greater

Step-by-step explanation:

7 plus 7 is greater than or equal to 14. Any number higher than 7 will still be correct, because it will be greater than 14. The little line on the bottom of the symbol means it can be equal to.

Hope this helps! If it does, please mark me brainliest. Thank you! ;)

Answer:

C i think

Step-by-step explanation:

Once an action is caused, a reaction immediatley happens

The given equation involves an integral of the function f(x) over a specific range. By applying the Fundamental Theorem of Calculus and evaluating the definite integral, we find that the result is \(-30 2 1 si f(x^3)xz dir 2\).

To calculate the final answer, we need to break down the problem and solve it step by step. Firstly, we observe that the limits of integration are given as 8 and 6° in the first integral, and 2 and 1 in the second integral. The notation "6°" suggests that the angle is measured in degrees.

Next, we need to evaluate the first integral. Since f(x) is continuous, we can apply the fundamental theorem of calculus, which states that if F(x) is an antiderivative of f(x), then ∫[a, b] f(x) dx = F(b) - F(a). However, without any information about the function f(x) or its antiderivative, we cannot proceed further.

Similarly, in the second integral, we have f(x³) as the integrand. Without additional information about f(x) or its properties, we cannot evaluate this integral either.

In conclusion, the final answer cannot be determined without knowing more about the function f(x) and its properties.

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Mr. Adam Bought 15 cookies and 10 muffins.

Variables to represent the number of muffins and cookies that Mr. Adam bought. We'll let x be the number of muffins and y be the number of cookies. Then we can set up two equations based on the information given:

Equation 1: x + y = 20   (the total number of muffins and cookies is 20)

Equation 2: 0.5y = 1.5x + 5   (the cost of the cookies is $5 more than the cost of the muffins)

Let's simplify Equation 2 by dividing both sides by 0.5:

y = 3x + 10

Now we can use substitution to solve for one of the variables. We can rearrange Equation 1 to solve for x:

x = 20 - y

Then we can substitute this expression for x in Equation 2:

y = 3(20 - y) + 10

Simplifying this equation, we get:

y = 50 - 3y

Adding 3y to both sides, we get:

4y = 50

Dividing both sides by 4, we get:

y = 12.5

This means that Mr. Adam bought 12.5 cookies. However, we can't have a fraction of a cookie, so let's check whether our solution makes sense in the context of the problem.

If Mr. Adam bought 12.5 cookies, he must have bought 7.5 muffins (since x + y = 20). But we can't have a fraction of a muffin either.

Therefore, it's likely that there was an error in the problem setup. One possibility is that Mr. Adam actually bought a total of 25 muffins and cookies (instead of 20). In this case, the equations would be:

Equation 1: x + y = 25

Equation 2: 0.5y = 1.5x + 5

Following the same steps as before, we would get:

y = 15 and x = 10

Therefore, Mr. Adam bought 15 cookies and 10 muffins.

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Answer:

Step-by-step explanation:

proucer surplus

Work Shown:

\(c^2 = a^2 + b^2 - 2ab\cos(C)\\\\c^2 + 2ab\cos(C) = a^2 + b^2\\\\2ab\cos(C) = a^2 + b^2 - c^2\\\\\boldsymbol{\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}}\\\\\)

Therefore, the probability that a randomly purchased item will last longer than 1 year is Probability ≈ 97.72%

To calculate the probability that an item will last longer than 1 year, we'll use the z-score formula. The z-score represents how many standard deviations an observed value is from the mean. The formula for the z-score is:
z = (X - μ) / σ
where X is the observed value (1 year), μ is the mean (2 years), and σ is the standard deviation (0.5 years).
Now, let's calculate the z-score:
z = (1 - 2) / 0.5
z = -1 / 0.5
z = -2
Next, we'll use a z-table to find the probability corresponding to the z-score of -2. The z-table value for -2 is 0.0228. Since we're looking for the probability that an item will last longer than 1 year, we need to consider the area to the right of the z-score, which can be calculated as:
Probability = 1 - 0.0228 = 0.9772

Therefore, the probability that a randomly purchased item will last longer than 1 year is Probability ≈ 97.72%

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Answer: A. There are many tangent lines that contain point A.

Step-by-step explanation:

Given, Point A is on circle O.

That means, Statement A. "There are many tangent lines that contain point A" is wrong.

The equation is b1 = 2Ah - b2

Note that the subject of formula is described as the variable that is made to stand alone on one of the equality sign.

From the information given, we have the equation as;

A = 1/2h(b1+ b2)

Such that the parameters are;

Now, make B1, the subject of formula;

cross multiply the values

2Ah = (b1+ b2)

collect the like terms

b1 = 2Ah - b2

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Answer:

Cir = d\(\pi\)

C = 15\(\pi\)

Step-by-step explanation:

Answer:

Exact Answer: 15π inches

Decimal Answer: 47.1 inches

Step-by-step explanation:

The unit is inches because circumference is one dimension.

1.) Circumference Formula: 2πr or dπ⇒d=diamater ⇒r=radius

2.) dπ=15π

3.) 15 × 3.14⇒approximate answer

Answer:

Step-by-step explanation:

Use the law of cosines to find the side AB:

Use the Heron's area formula next:

Now

Next

Substitute this into the first equation:

Answer:

AB = 7 cm

Step-by-step explanation:

Sine Rule for Area

\(\sf Area =\dfrac{1}{2}ab \sin C\)

where:

Given:

Substitute the given values into the formula and solve for x:

\(\begin{aligned} \sf Area & = \dfrac{1}{2}ab \sin C \\\\\implies \sqrt{300} & = \dfrac{1}{2}(x+3)x \sin 60^{\circ}\\\\\sqrt{300} & = \dfrac{\sqrt{3}}{4}(x+3)x\\\\\dfrac{4\sqrt{300}}{\sqrt{3}} & = x^2+3x\\\\40 & = x^2+3x\\\\x^2+3x-40 & = 0\\\\ (x-5)(x+8)& = 0\\\\ \implies x & = 5, -8\end{aligned}\)

As length is positive, x = 5 only.

Substitute the found value of x into the expressions for the side lengths:

Cosine rule

\(c^2=a^2+b^2-2ab \cos C\)

(where a, b and c are the sides and C is the angle opposite side c)

Substitute the found values into the formula and solve for AB:

\(\begin{aligned}c^2 & =a^2+b^2-2ab \cos C\\\implies AB^2 & =8^2+5^2-2(8)(5) \cos 60^{\circ}\\AB^2 & =89-40\\AB^2 & =49\\AB & =\sqrt{49}\\AB & = \pm 7\end{aligned}\)

As length is positive, AB = 7 cm.

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Answer:

Step-by-step explanation:

To find the value of x, solve the equation. Do this by rearranging the equation to make x the subject.

Answer:

x=32761 /4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4x+7=32768

Step 2: Subtract 7 from both sides.

4x+7−7=32768−7

4x=32761

Step 3: Divide both sides by 4.

Answer:

x = -9

Step-by-step explanation:

7x = 6x - 9

-6x   -6x

x = -9

(i) The value of g(3, 2, 1) is 0, and the gradient of g at (3, 2, 1) is N = ∇g(3, 2, 1).

(ii) The symmetric equation of the line L through (3, 2, 1) in the direction of N is given. Also, the canonical equation of the plane through (3, 2, 1) normal to N is provided.

(i) To show that g(3, 2, 1) = 0, we substitute the given values into the expression for g: g(3, 2, 1) = (3)(2)(1) - 6 = 0, confirming that g(3, 2, 1) equals zero. The gradient of g, denoted as ∇g(x, y, z), represents the vector of its partial derivatives. Evaluating ∇g at (3, 2, 1), we obtain N = ∇g(3, 2, 1).

(ii) The symmetric equation of a line L passing through a point \((x_0, y_0, z_0)\) in the direction of a vector N = <a, b, c> is given by the parametric equations: x = \(x_0\) + at, y = \(y_0\) + bt, z = \(z_0\) + ct. Plugging in the values (3, 2, 1) for \((x_0, y_0, z_0)\) and the components of N from part (i), the symmetric equation of the line L is obtained.

For the canonical equation of a plane, we know that a plane with a normal vector N = <a, b, c> passing through a point \((x_0, y_0, z_0)\) has the equation ax + by + cz = d, where d is a constant. Substituting the values (3, 2, 1) for \((x_0, y_0, z_0)\) and the components of N from part (i), we can find the canonical equation of the plane.

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The function g(x, y, z) = xyz - 6 evaluates to zero when x = 3, y = 2, and z = 1. The gradient vector ∇g(x, y, z) at (3, 2, 1) can be found. The symmetric equation of the line L passing through (3, 2, 1) in the direction of the gradient vector is determined, along with the canonical equation of the plane through (3, 2, 1) that is perpendicular to the gradient vector.

To show that g(3, 2, 1) = 0, we substitute the given values into the expression for g(x, y, z): g(3, 2, 1) = 3 * 2 * 1 - 6 = 0.

The gradient vector ∇g(x, y, z) represents the vector of partial derivatives of g(x, y, z). In this case, ∇g(x, y, z) = (yz, xz, xy). Evaluating at (3, 2, 1), we get ∇g(3, 2, 1) = (2 * 1, 3 * 1, 3 * 2) = (2, 3, 6).

The symmetric equation of a line passing through a given point (x₀, y₀, z₀) in the direction of a vector (a, b, c) is given by (x - x₀)/a = (y - y₀)/b = (z - z₀)/c. Substituting the values (3, 2, 1) and (2, 3, 6), the symmetric equation of the line L through (3, 2, 1) in the direction N is (x - 3)/2 = (y - 2)/3 = (z - 1)/6.

The canonical equation of a plane passing through a given point (x₀, y₀, z₀) and perpendicular to a vector (a, b, c) is given by a(x - x₀) + b(y - y₀) + c(z - z₀) = 0. Substituting the values (3, 2, 1) and (2, 3, 6), we obtain the canonical equation of the plane through (3, 2, 1) that is normal to N as 2(x - 3) + 3(y - 2) + 6(z - 1) = 0.

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Answer:

Step-by-step explanation:

The Internal Rate of Return (IRR) is a financial metric used to estimate the profitability of an investment. To find the Internal Rate of Return (IRR) for an investment where an investor lends $10,000 and receives $7,000 at the end of year 2.

The Internal Rate of Return (IRR) is a financial metric used to estimate the profitability of an investment. It represents the discount rate at which the present value of cash inflows equals the present value of cash outflows. In this case, the investor lends $10,000 (cash outflow) and receives $7,000 (cash inflow) at the end of year 2.

To calculate the IRR, we need to determine the discount rate that makes the net present value (NPV) of the cash flows equal to zero. In other words, we need to find the discount rate that equates the present value of $7,000 at the end of year 2 with the present value of the initial investment of $10,000.

Using a financial calculator or spreadsheet software, we can use the trial-and-error method or built-in functions to find the IRR. By adjusting the discount rate, we can determine the rate at which the NPV becomes zero. In this case, the IRR represents the annualized return on the investment that would make the present value of cash inflows equal to the initial investment of $10,000.

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A basis for the null space of the matrix is the vector [-1, 2, 1].

To find a basis for the null space of the matrix:

[ 0  1 -2 ]

[ 4  3 -5 ]

[ 1 -2  0 ]

We need to find the vectors x such that Ax = 0, where 0 is the zero vector. In other words, we need to solve the system of linear equations given by:

0x + y - 2z = 0

4x + 3y - 5z = 0

x - 2y + 0z = 0

We can start by using row reduction to put the matrix in reduced row echelon form:

[ 1  0  1 ]

[ 0  1 -2 ]

[ 0  0  0 ]

From the last row, we can see that z is a free variable, so we can choose any value for z. Then, using the first two rows, we can express x and y in terms of z:

x = -z

y = 2z

Therefore, the null space of the matrix consists of all vectors of the form:

[ -z ]

[ 2z ]

[ z  ]

We can verify that this is indeed the null space of the matrix by multiplying it by the original matrix and verifying that the product is the zero vector. For example, let's take z=1:

[ 0  1 -2 ]   [ -1 ]   [ 0 ]

[ 4  3 -5 ] * [  2 ] = [ 0 ]

[ 1 -2  0 ]   [  1 ]   [ 0 ]

Therefore, a basis for the null space of the matrix is the vector [-1, 2, 1].

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(a) The function f(x, y) does not have a limit at (0,0). (b) No information is provided to determine the limit for f2(x, y).

(a) For the function f(x, y) = 5ry²/(3x² + y²), we can analyze the behavior as (x, y) approaches (0,0). Since the denominator 3x² + y² becomes zero as (x, y) approaches (0,0), we cannot directly evaluate the function at this point. However, by considering the parabola z = -y², we can observe that the function does not approach a specific value and thus does not have a limit at (0,0).

(b) The function f2(x, y) = Vel + Vsin(y) is not well-defined as no information or context is provided for the variables Vel, V, and U. Without this information, it is not possible to determine the limit of the function at (0,0) or any other point.

Therefore, for (a), the function f(x, y) does not have a limit at (0,0), and for (b), no information is given to determine the limit for f2(x, y).

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the area of the region that lies inside the first curve r = 17sin(θ) and outside the second curve r = 9 - sin(θ) is (399π + 5√3)/2.

To find the area of the region that lies inside the first curve r = 17sin(θ) and outside the second curve r = 9 - sin(θ), we need to determine the limits of integration for θ and set up the integral in polar coordinates.

First, let's find the intersection points of the two curves:

17sin(θ) = 9 - sin(θ)

Rearranging the equation:

18sin(θ) = 9

sin(θ) = 1/2

θ = π/6 or π/2

Now, we can set up the integral to find the area:

A = ∫[θ1,θ2] ½ r^2 dθ

where θ1 = π/6 and θ2 = π/2 are the limits of integration, and r is the outer curve minus the inner curve.

A = ∫[π/6,π/2] ½ ( (9 - sin(θ))^2 - (17sin(θ))^2 ) dθ

Simplifying the integral:

A = ∫[π/6,π/2] ½ ( 81 - 18sin(θ) + sin^2(θ) - 289sin^2(θ) ) dθ

A = ∫[π/6,π/2] ½ ( 81 - 18sin(θ) - 288sin^2(θ) ) dθ

Evaluating the integral:

A = ½ [81θ - 18cos(θ) - 96/3 sin^3(θ)] | [π/6,π/2]

A = ½ [(81π/2 - 18cos(π/2) - 96/3 sin^3(π/2)) - (81π/12 - 18cos(π/6) - 96/3 sin^3(π/6))]

Simplifying further:

A = ½ [(81π/2 - 0 - 0) - (81π/12 - 18(√3/2) - 96/3 (1/8√3))]

A = ½ [(81π/2) - (81π/12) + 9√3 - 4√3]

A = ½ [((81*6π) - (81π) + 5√3)]

A = ½ (480π - 81π + 5√3)

A = ½ (399π + 5√3)

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Answer:

quadratic

Step-by-step explanation:

Answer:

In simple terms, it basically means to select the important parts of the data and take note of them. It's a very helpful technique.

On the cherry - picking mean in the context of data analytics is confirmation bias. The correct option is (B)

Cherry picking is the selective use of evidence to support a claim while ignoring other data that is more likely to challenge that claim.

here, we have,

It's not always done with malicious purpose, but this behavior is extremely widespread. Probably even you have cherry-picked.

now, we know that,

cherry picking looks  like as:  

For instance, someone who cherry picks may only mention a few studies out of the many that have been published on a certain topic in an effort to make it appear as though the scientific consensus supports their position.

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so let's notice that, the equation is f(x) in x-terms, meaning the variable "x" is the independent and thus the parabola is a vertical parabola.  Also let's notice that the equation is already in vertex form, keeping in mind that the  axis of symmetry occurs for a vertical parabola at the x-coordinate.

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2(x-\stackrel{h}{5})^2+\stackrel{k}{8}~\hfill \stackrel{vertex}{(5,8)}~\hfill \stackrel{\textit{equation for axis of symmetry}}{x=5}\)