what are the steps to convert a quadratic function in standard form to vertex form
Answers
Alternately, you can calculate the value for the vertex as such using this formula for the ordered pair: [tex]( \frac{-b}{2a}, f(\frac{-b}{2a}))[/tex]. Then, you can plug this point in for [tex](h, k)[/tex].
To convert a quadratic function in standard form to vertex form, follow these steps: identify the given equation, find the x-coordinate of the vertex, substitute the x-coordinate to find the y-coordinate, and write the function in vertex form.
Explanation:To convert a quadratic function in standard form to vertex form, follow these steps:
Identify the given equation in standard form, which is in the form of ax² + bx + c = 0.Use the formula x = -b/2a to find the x-coordinate of the vertex.Substitute the found x-coordinate into the original equation to find the y-coordinate of the vertex.Write the quadratic function in vertex form as y = a(x-h)² + k, where (h, k) is the vertex of the parabola.For example, if the quadratic function is given as 2x² - 8x + 5 = 0, we first find the x-coordinate of the vertex using the formula x = -b/2a as x = -(-8)/(2*2) = 2. Substituting this x-coordinate into the equation, we find the y-coordinate of the vertex as y = 2*(2)² - 8*(2) + 5 = -3. Therefore, the quadratic function in vertex form is y = 2(x-2)² - 3.
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Related Questions
The cost, in dollars, to rent a kayak is proportional to the number x of hours you rent the kayak. It costs $27 to rent the kayak for 3 hours. Write an equation that represents y.
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A pitcher contains 1 3/4 quarts of milk. How many fluid ounces of milk does the pitcher contain ?
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1 3/4 quarts is equivalent to 56 fluid ounces. This conversion is done by first converting the mixed fraction to an improper fraction, and then multiplying by 32, which is the number of ounces in one quart.
Explanation:The subject of your question is Mathematics, specifically a unit conversion problem. You want to convert 1 3/4 quarts of milk to fluid ounces. We know that there are 32 fluid ounces in one quart. So, to convert quarts to fluid ounces, we multiply the number of quarts by 32:
For 1 3/4 quarts:
1. First, convert the mixed fraction to an improper fraction: (1 * 4) + 3 = 7/4 quarts
2. Multiply by 32(our conversion factor from quarts to fluid ounces): (7/4) * 32 = 56
So, 1 3/4 quarts is equal to 56 fluid ounces.
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What is the first step in simplifying the expression 11x-2-3(1-7x)^2+(x+1)
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Answer with Step-by-step explanation:
We are given a expression:
[tex]11x-2-3(1-7x)^2+(x+1)[/tex]
We have to determine the first step in the solution of the above expression.
First step will be to solve the term [tex](1-7x)^2[/tex]
We will firstly square the term 1-7x
[tex]11x-2-3(1-7x)^2+(x+1)\\\\=11x-2-3(1+49x^2-14x)+(x+1)\\\\=11x-2-3-147x^2+42x+x+1\\\\=-147x^2+54x-4[/tex]
Hence, First step is:
solve the term [tex](1-7x)^2[/tex]
emilys meal costs 32.75 and darren's meal costs 39.88. emily treats darren by paying for both meals, and leaves a 14 percent tip. find the total cost
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82.80
32.75+39.88=72.63
72.63x1.14=82.7982 rounds to 82.80
What is 871 rounded to the nearest ten
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It is 870.
Hope This Helps You!
Good Luck :)
- Hannah ❤
Rounding 871 to the nearest ten gives us 870.
We have,
To round 871 to the nearest ten, we look at the ones digit, which is 1.
If the ones digit is 5 or greater, we round up to the next ten.
If the ones digit is less than 5, we round down to the previous ten.
In this case, the ones digit is 1, which is less than 5.
Therefore, we round down.
Rounding 871 to the nearest ten gives us 870.
Thus,
Rounding 871 to the nearest ten gives us 870.
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You purchasing 220 airline ticket you have a discount code to receive 10% off there is a 10.5% service charge and how much do you pay for your ticket
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But you have to pay 10.5% service charge, that means the service charge is 198x10.5%= 20.79
And finally you have to pay: 198+20.79= 218.79
Hope it is helpful
There are 20 people in Susan’s class. Each person gives a card to everyone else in the class. How many cards were exchanged?
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⇒20*19=380 card were exchanged
a cabbage palmetto has a height of 80 feet. what is the approximate height of the tree in meters?
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If the height of the cabbage palmetto is 80 feet, it should be about 80*0,3 = 24 meters.
So a cabbage palmetto with 80 feet of height is about 24 meters.
Hope this helps! :)
A circuit board manufacturer can produce 2,000 boards per hour. How many days will it take to produce 16,500 if the company has a 10 hour work shift? How many days will it take to produce 16,500?
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OK so 2,000 boards per hour in 10 hours is 2,000*10=20,000 boards in 10 hours. So it can produce 16,500 boards in less than a day.
I may be wrong but I hope this helps!
Answer:
it will take less than one day.
Step-by-step explanation:
A circuit board manufacturer can produce 2,000 boards per hour.
If the company has a 10 hour work shift.
manufacturer can produce in one day = 2000 × 10 = 20,000
To produce 16,500 boards, they need time = 16,500 ÷ 2000 = 8.25 hours
The company will take to produce 16,500 boards in 8.25 hours less than one day.
amanda read 15 pages of her 150-page book in 2 hours. At this rate, how long will it take her to read the entire book?
Answers
The answer to your question will be 20 hours!
Glad to help :)
Each year a school sends 50 students to a conference. Last year, the cost was $12.50 per student. This year, the cost per student has increased by 16%. How much will it cost to send 50 students to the conference this year
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multiply 12.50 by 16% to find the new cost
12.50 * 1.16 = 14.50 per student
14.50 * 50 = $725
This year, each student has to pay $14.5.
14.5 * 50= 145*5= $725
need help like last time do the same thing
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He collected 1 1/3
6) 60/10=6
They sold 6 cats per week
7) 90/10=9
He/she installed 9 sheets per minute.
I need the answer for #4 a&b
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What factor makes the number true
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1. Write the square of 6
2. Write the number of terms in 6x + 3y
3. Simplify 3x + 2y + y + 4x
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2. 6x+3y =9
3.3y+7x
In a board game, negative number cards represent moving backward and positive number cards represent moving forward. For example, Nuha drew a card with 4 and moved forward 4 spaces.
Rags draws a card with 0.
What does 0 represent in the board game?
Choose 1 answer:
A: Not moving any spaces
B: The number of spaces she moved on her last turn.
C: Losing all points.
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how will i do this it is very confusing.
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A scale factor is a term that defines the multiplicative/divisive measurement difference between the two same shapes. The way we can find our scale factor is by dividing our new measurement by the old measurement.
681 / 3 = 227
Our scale factor is 1/227, as 3 is 1/227 of 681 - and we are looking for the scale factor to find what multiplied by 681 would give us 3.
I hope this helps!
if cosA=2/5, find the value of 4+4 tan^2A
Answers
cos A = 2/5
A = cos⁻¹(2/5) = 66.42°
Now that we know A, we use this value to the second equation.
4 + 4tan²A = 4 +24.996 4tan²(66.42°) = 24.996 ≈ 25
Answer:
25
Step-by-step explanation:
Solve the quadratic equation y2 - 5y = -4 by factoring.
Answers
y^2 - 5y + 4 = 0
(y - 4)(y - 1) = 0
y - 4 =0; y = 4
y - 1 =0; y = 1
answer
y = 4 and y = 1
y² - 5y +4 = 0
y -4
y -1
(y - 4)(y - 1)
y = 4 , 1
hope this helps
Solve for x in the diagram shown.
A) 15
B) 16(mixed fraction
1
3
C) 16 (mixed fraction)
2
3
D) 17
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Then multiply that by the 20 to get: 16.6666667 or as a fraction 16 2/3
Final answer: C.) 16 2/3
Hope this helps!
The value of x will be 16 2/3.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
LMN is a triangle shown in figure.
Now,
Here, LMN is a triangle shown in figure.
By definition of proportionality, we get;
⇒ x / 15 = (20 + x) / (15 + 18)
Solve for x as;
⇒ x / 15 = (20 + x) / 33
⇒ 33x = 15 (20 + x)
⇒ 33x = 300 + 15x
⇒ 33x - 15x = 300
⇒ 18x = 300
⇒ x = 300/18
⇒ x = 50/6
⇒ x = 16 2/3
Thus, The value of x will be 16 2/3.
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eight cheerleaders set a goal of selling 424 boxes of cards to raise money. after two weeks, each cheerleader has sold 28 boxes. how many boxes more must each cheerleader sell?
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yesterday jamal scored -20 points on a puzzle today he scored more points use absolute value to describe today's score as a loss
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The absolute value of Jamal's score is 20, indicating a loss of 20 points.
Explanation:In math, the absolute value of a number is the positive value of that number, regardless of its sign. Since Jamal's score on the puzzle was -20 points, we can use absolute value to describe today's score as a loss by taking the absolute value of the score. The absolute value of -20 is 20, which means that today's score was a loss of 20 points.
I really need help
thx
Answers
over which equals 10/40 or 1/4
5*8
6)8*3=24
15*10=150 answer is 24/150
7)2*12=24
9*13=117 answer 8/39
8)7*12=84
8*1=8 answer 8 and 1/2 or 84/8
9)4*5=20
12*1=12 answer 1and 2/3 or 20/12
10) 4*4=16
9*9=81 answer 16/81
11)3*7=21
14*9=126 answer 1/6
12)8*24=192
9*11=99 answer 1 and 31/33 or 192/99
Choose the correct description of the graph of the compound inequality 3x + 1 > 10 and 4x alt= 20.
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Unit rate 117 points in 13 minutes
Answers
Divide 117 by 13 to get your answer.
Answer: 9 points per minute.
Step-by-step explanation:
Hi, answer this question we have to calculate the unite rate in points per minute; by dividing the number of points (117) by the number of minutes.
Mathematically speaking:
117 points / 13 minutes = 117/13= 9 points per minute
So, the unit rate is 9 points per minute.
Feel free to ask for more if needed or if you did not understand something.
solve the system by the elimination method? -5x-2y=2 6x-2y=24
Answers
Make either x or y opposites and then solve.
Hope this helps.
6x-2y=24
Notice that -2y appears in both equations. Multiply the first equation by -1, obtaining
5x + 2y = -2 and then adding the second equation to this result:
6x -2t = 24
-----------------
11x = 22, so x = 2. Now subst. 2 for x in either of the original equations to find the value of y.
6(2) - 2y = 2 becomes 2y = 12-2, or 2y = 10, or y = 5.
Solution is (2,5). You MUST check this, however.
-Question Worth 50 Points-
At the city park there were 15 blue jays, 6 cardinals, and 9 mockingbirds.
For each of the following questions set up a proportion equation and solve for the unknown.
1. If there were 6 mockingbirds, how many cardinals would there be at the park?
2. If there were 5 blue jays, how many cardinals would there be at the park?
3. If there were 20 cardinals, how many mockingbirds would there be at the park?
Answers
6 mockingbirds is 2/3 of 9
so 2/3 of 6 is 4 cardinals
5 blue jays is 1/3 of 15
so 1/3 of 6 cardinals is 2 cardinals
There are 20 cardinals, how many mockingbirds.
the ratio is 2/3, so 20/30 is your answer
hope this helps
Solve for x:
x + 4.5 = -17.75
Please help!
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Given the functions f(x) = − 4x − 1 and g(x) = 2x + 4, which operation results in the smallest coefficient on the x term?
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Answer: addition
Step-by-step explanation:
what is 65% of 300!???
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65% of 300 is 195.
300 * 65% = 195