When the function is given in vertex form y=a(x-h)2+k, how is the vertex found?

Answers

Answer 1
Once you have it in that form, you just read off the values of h and k

For instance, if you had y = 2(x-3)^2 + 5, then h = 3 and k = 5. So the vertex is (h,k) = (3,5)
Answer 2

Answer:

Given function is [tex]y=a(x-h)^2+k[/tex] ...........(1)

We re write the function,

transfer k to LHS,

[tex]y-k=a(x-h)^2[/tex]

Since, One variable has degree 2 and one variable has degree 1.

Function Represent the equation of Parabola.

In given Function,

Coordinates of vertex is ( h , k )

So To, find the vertex of the function.

First we rewrite the function in vertex form that is like equation (1) then we compare them and write the coordinate of the vertex.

For Example,

1. y = 2(x - 2)² + 6 then vertex of the function is ( 2 , 6 )

2. y = -3 ( x + 3 )² - 6

    y = - 3 ( x - (-3) )² + ( -6) then vertex of the function is ( -3 , -6 )


Related Questions

Identify the variation as direct, inverse, joint or combined.
The cost of the number of the same articles purchased varying with the number purchased.
a.direct
b.inverse
c.joint
d.combined ...?

Answers

a. direct variation
A relationship between two variables in which one is a constant multiple of the other. 

Answer:

The statements " cost of the number of the same articles purchased varying with the number purchased' shows direct variation .

Option (a) is correct .

Step-by-step explanation:

Definition of the direct variation

When two variables that can be expressed by an equation in which one variable is equal to a constant times the other.

i.e

[tex]x \propto y[/tex]

x = ky

As the x increases than y is also increase .

As given the statement in the question

The cost of the number of the same articles purchased varying with the number purchased.

i.e

As the number of purchased article increases thus cost of the articles also increases .

Therefore the statements " cost of the number of the same articles purchased varying with the number purchased' shows direct variation .

Option (a) is correct .

Dion practiced the long jump . he jumped 3.05 meters,2.74 meters and 3.3 meters.what was the average length of dion's jumps?

Answers

3.05 + 2.74 + 3.3 = 9.09
divide that by 3 or basically how many numbers
9.09÷3= 3.03 this is your average

translate the following into interval notation: "The union of all numbers greater than eight, and less than or equal to negative four".

Answers

() is for <>
[] is for ≤≥


greater than 8 means
x>8 or
8 to infinity not counting 8 or
(8,∞)

less than or equal to -4 is
x≤-4 or
from -∞ to -4
or
(-∞,-4]

the infinity has a () sign since you cannot equal infinity, you can approach it

U is unity so

(-∞,-4] U (8,∞)

which expression equivalent to k^1/4 · cubed root of k^2

Answers

From the info i'm getting, the best answer is ought to be B, because of increase in the denominator & it's numerator! It keeps the same pace as 1/4.

I do recommend to double check this with a classmate!

If not B, then my best guess is A.

If segment UV is considered to be the base of parallelogram TUVW, which segment would represent the altitude of the parallelogram?

segment TU

segment TX

segment WT

segment WV

PLEASE HELP ...?

Answers

The best and most correct answer among the choices provided by your question is the second choice or letter B.

Segment TX is the segment that would best represent the altitude of the parallelogram.

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The sides of the cubes are numbered 1 through 6. If they are both tossed, what is the probability that they will both be a 2?

Answers

The best waay to get to this result is using the formula and the numbers
(1/6)^2=1/36
so the porbability would be 1 out of 36

Answer:

The answer is 1/36

Step-by-step explanation:

number is a factor of 51?

Answers

Only 1 and 51 are factors of 51. 

What is the range of y = sin θ ?

Answers

The range of a function is the set of all the possible function outputs. We know that sin theta varies between -1 and 1 if we draw a graph. According to the graph, the largest number that is an output of g is -1, and the smallest number is 1. Every number between them is also an output of g for some input. Therefore, the range of g is [-1,1]. 


The range of y=sin θ :
1 ≤ y ≤ 1

A triangle has sides of length 3 cm and 10 cm. What can you say about the length of the third​ side?

Answers

The inequality that represents the third side of the triangle is the third side < 13.

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

Given, A triangle has sides of length 3 cm and 10 cm.

From the rule of the triangle, The sides of a triangle rule assert that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.

thus, we can say that

third side < 10 + 3

third side < 13

Therefore, The inequality third side < 13 is used to represent the triangle's third side.

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Final answer:

Using the Triangle Inequality Theorem, the third side of a triangle with sides of 3 cm and 10 cm must be greater than 7 cm and less than 13 cm.

Explanation:

To determine the possible length of the third side of a triangle given two side lengths of 3 cm and 10 cm, we use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the third side must be longer than 7 cm (10 cm - 3 cm) but shorter than 13 cm (10 cm + 3 cm).

Simplify the expression

sin(pi+x) + sin(pi - x)
...?

Answers

The solution to the problem is as follows:

sin(π+x) = -sin(x) and sin(π-x)= sin(x) 

sin(π+x) + sin(π-x) = -sin(x) + sin(x) 

=  0


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Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by five. How do you do this? :/

Answers

[tex]\theta= \frac{\pi}{5} [/tex]
[tex]\\ \theta_1,\theta_2[/tex] - coterminal angles

[tex]\\ \theta_1= \frac{\pi}{5} +2\pi= \frac{\pi}{5} + \frac{10\pi}{5}= \frac{11\pi}{5} \\ \\ \theta_2= \frac{\pi}{5} -2\pi= \frac{\pi}{5} - \frac{10\pi}{5}=- \frac{9\pi}{5} [/tex]

Write the equation y-2=6x 3 in y mx b form

Answers

the correct answer is y= 6x+1

Final answer:

The equation y - 2 = 6x is rewritten in the y = mx + b form by simply adding 2 to both sides resulting in y = 6x + 2, where 6 is the slope and 2 is the y-intercept.

Explanation:

The equation y - 2 = 6x is not fully written in the y = mx + b form, which is the standard form of a linear equation where m represents the slope and b represents the y-intercept. To convert the given equation into the y = mx + b form, we need to isolate y on one side of the equation.

First, we will add 2 to both sides of the equation:

y - 2 + 2 = 6x + 2

Which simplifies to:

y = 6x + 2

Now we have written the equation in the desired form, with m = 6 and b = 2. This linear equation represents a line with a slope of 6 and a y-intercept at (0, 2). Graphically, the line can be plotted using these values, and a table of points can be created by plugging various x values into the equation.

explain the difference between 1/(sinx) and ((sin^-1)x) ...?

Answers

1/sin(x) is the inverse of the entire value of sin(x), while sin⁻¹(x) is the inverse of the value of x. These are different operations so yield different answers. For example, let x = π/2
1/sin(π/2) = 1
sin⁻¹(π/2) does not exist because π/2 lies outside the range of sin(x).

The maximum gas mileage for a compact car is estimated using the graph shown below.


The average gas mileage for an SUV is modeled by the function m(s)=−0.015(s−55)2+15, where s is the SUV's speed in miles per hour.


The difference in maximum mileage between these two vehicles is _____ mpg (miles per gallon).


Enter the number that correctly fills in the blank in the previous sentence.

Answers

the graph's maximum is at 33 mpg for reference −0.015(x−55)2+15so just plug it inlet's set y to 0

y=−0.015(x−55)2+15 0=−0.015(x−55)2+15 subtract 15 −15=−0.015(x−55)2 divide both sides by -0.015 1000=(x−55)2
the other maximum is at x=55
and we want the y value
at x=55, y=-0.015(55-55)^2+15 y=-0.015(0)+15 y=15
 the compact has a max of 33mpg and the SUV 15mpg

so you would subtract the 33 and the 15

A model is made of a car. The car is 8 FEET long and the model is 10 INCHES long. What is the ratio of the length of the car to the length of the model? a)10:8 b)48:5 c)5:48 d)8:10

Answers

correct answer
is D 8:10

Answer:

8:10

Step-by-step explanation:

Given: line DR tangent to Circle O.

If m angle C = 63°, then m angle BDR =

Answers

Based on the given figure above, we can say that the measure of angle BDR is also 63°. R is meant to be tangent to the circle so, this makes the angle BDR equal to C. Angle C is half of the arc as well as BDR. Hope this is the answer that you are looking for. 

Answer:

m∠BDR=63°  

Step-by-step explanation:

It is given that  line DR tangent to Circle O and m∠BCD=63°, then the measure of the angle BDR can be determined as:

Since, angle BDR is made between the chord and the tangent, and we know that the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment, therefore

m∠BCD=m∠BDR=63°

Hence, the measure of angle BDR=63°.

What is the average rate of change for the sequence shown below?

coordinate plane showing the points 1, 4; 0.5, 3.5; 0, 3; and negative 0.5, 2.5

−2
−one half
1
2

Answers

Let's pick on two points. Let's say we pick the first two points which are (1,4) and (0,5,3.5)

The slope formula tells us that

m = (y2-y1)/(x2-x1)
m = (3.5-4)/(0.5-1)
m = (-0.5)/(-0.5)
m = 1

So the slope is 1. We can pick any other two points, run them through the slope formula, and we'll get the same result. 

So that's why the answer is choice C) 1

Answer:

1

Step-by-step explanation:

Step 1: Select 2 points  

(0,3)     (0.5, 3.5)

x1,y1     x2,y2

Step 2: use average rate of change formula

[tex]\frac{y2-y1}{x2-x1}[/tex] = average rate of change

[tex]\frac{3.5-3}{0.5-0} =\frac{0.5}{0.5} =1[/tex]

which of the following functions is graphed below??

Answers

Final answer:

Without seeing the actual graph, it's impossible to provide an accurate response. However, several common types of function graphs have been described.

Explanation:

Unfortunately, without seeing the graph in question, it is not possible to provide an accurate response to your question regarding which function is graphed. However, we can discuss what a few different types of common functions might look like.

A straight line with a positive slope from the lower left to the upper right indicates a direct relationship between x and y values, such as y = x or y = 2x + 1.

A curved graph that resembles a U shape either upright or upside down might suggest a quadratic function such as y = x^2 or y = -x^2.

As for time-graphs, the gradient of a velocity-time graph gives acceleration, while the area under the velocity-time graph gives displacement. The gradient of a position-time graph gives velocity.

Supply and demand curves are graphs used in economics. The supply curve typically slopes upward, and the demand curve usually slopes downward.

Without seeing the actual graph or having more details, this is the best general information that can be provided.

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The piecewise-defined function that is graphed below include the following: D. [tex]f(x)=\left\{\begin{array}{Ir}x^3-3, & x \leq 2\\x^2+6, & x > 2\end{array}\right[/tex]

In Mathematics and Euclidean Geometry, a piecewise-defined function is a type of function that is defined by two or more mathematical expressions over a specific domain.

Note: The inequality symbol < or > represents a hollow dot (circle).

The inequality symbol ≤ or ≥ represents a solid dot (circle).

Generally speaking, the domain of any piecewise-defined function is the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, there is a solid circle above 2 that decreases to the left and a hollow circle above 2 that increases to the right.

In this context, the piecewise-defined function is defined over the following domains;

Domain = x ≤ 2, for [tex]f(x) = x^3 - 3[/tex].

Domain = x > 2, for [tex]f(x) = x^2+6[/tex].

Complete Question:

Which of the following functions is graphed below?

Solve the equation

x^2 + 5x + 4 = 0

Answers

x^2 + 5x + 4 = 0
(x + 4)(x + 1) = 0

x + 4 = 0
x = -4 <===

x + 1 = 0
x = -1 <===

Step-by-step explanation:

answer:

x^2 + 5x + 4 = 0

x²+4x+x+4=0

x(x+4)+1(x+4)=0

(x+4)(x+1)=0 is your answer

At president bush's inauguration in 2005, the newspaper headline stated there were about 400,000 people in attendance at the newspaper rounded to the nearest 10,000 what is the largest number and smallest number of people who could have been there

Answers

largest = 405,000
smallest  = 395,000

Answer:

At president bush's inauguration in 2005, the newspaper headline stated there were about 400,000 people in attendance.

Now, rounding to nearest ten thousand the greatest number will be: 404999.

And the smallest number will be : 395000

So, the largest number of people who could have been here is 404999.

And the smallest number of people who could have been here is 395000.

describe how to draw a line that passes through the origin and has a slope of 3/5

Answers

A slope of 3/5 means it rises 3 units and runs 5 units. Thus, to draw such a line, we go up three units from the origin and go to the right 5 units after this point. The point obtained will be one point on the line. We continue this procedure for two to three points and then join them to obtain a line.

Each ratio in simplest form 16:40

Answers

16:40 = 4:10 = 2:5

hope this helps you

Which set of line segments with the given lengths can be formed into a right triangle?

24,30,35
12,18,30
18,24,30
18,24,35 ...?

Answers

a² = b² + c²

30² = 18² + 24²

18, 24, 30

Answer:

there right

Step-by-step explanation:

When the function below is graphed, how many x-intercepts does it have? y = 2x2 - 8x + 5

Answers

It has two x-intercepts because the exponent of the equation is 2 and the graph crosses the x-axis twice

Answer:

2.

Step-by-step explanation:

Please find the attachment.

We have been given a function formula [tex]y=2x^2-8x+5[/tex]. We are asked to determine the number of x-intercepts that our function could have by graphing.

Since our given function is a quadratic function, so it could have at-most two x-intercepts as it will cross x-axis at-most two times.

Upon looking at our attached graph we can see that our given function crosses x-axis at two points, therefore, our given function has two x-intercepts.

Eugenia wants to find out how fast she walked along the hiking trail that took her 1.5 h to complete. She counted the number of steps with a pedometer and got 10000 steps. in order to calculate the distance she walked she estimated the length of her stride. she walked 10 steps three times at her usual rate and measured the distance with a measuring tape (the smallest division is 1cm) and got 745cm, 748 cm, 739 cm. Find the length of her stride. What is the length of the hiking trail? What are absolute and relative uncertainties in that length?

Answers

1) length of her stride

- 745/10 = 74.5

- 748/10 = 74.8

-739/10 = 73.9

Average: 74.5 + 74.8 + 73.9]/3 = 74.4 cm

2) length of the hiking trial

74.4 cm/step * 10,000steps = 744,000 cm = 7,440 m = 7.4 km

3) Absolute error

legnth with the smallest step measure: 73.9 * 10,000 = 739,000 cm

length with the largest step measure: 74.8 * 10,000 = 748,000 cm

maximum error 744,000cm - 739,000cm = 5,000 cm

4)  relative error

[absolute error / measure] * 100

[5,000 cm / 744,000 cm] * 100 = 0.67%

Find tan θ if sec θ = (sqrt26)/5 and sin θ < 0.

Answers

so cos θ = 5/sqrt(26)
adjacent = 5
hypotenuse = sqrt 26
by pythagoras opposite = 1
so sin θ = 1/sqrt (26)
and tan θ = 1/5

True or False?
(a^4)(a^5) = (a)^9

Answers

The above result is true according to the property [ a^x. a^y = a^ (x+y)].

A candy company used 8 gallons of syrup to make 4 batches of candy. what is the rate of syrup per batch.

Answers

8 gallons syrup to 4 batches of candy....8/4 = 2 gallons of syrup to 1 batch of candy...so ur ratio is : 2/1 or 2:1 or 2 to 1

How do you solve (a^3b)^4(ab^6)^2?

Answers

I hope this helps you

Divide 28x3 + 42x2 - 35x by 7x

Answers

(28x³ + 42x²– 35x)/(7x) = 28x³/(7x) + 42x²/(7x) + 35x/(7x) = 4x² + 6x + 5
The answer is [tex]4 x^{2} +6x-5[/tex]

[tex] \frac{28 x^{3} +42 x^{2} -35x}{7x} = \frac{28 x^{3} }{7x} + \frac{42 x^{2} }{7x} - \frac{35x}{7x} =4 x^{2} +6x-5[/tex]
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