Describe the three forms of a quadratic function. Identify the vertex and axis if symmetry of each form. Which form do you prefer and why?
Answers
Explanation
The three forms of the quadratic equation can be given as
Part A
1) Standard Form
\(StandardForm:f(x)=ax^2+bx+c\)2) Factored form
\(FactoredForm:f(x)=a\left(x-p\right)\left(x-q\right)\)3) Vertex form
\(VertexForm:f(x)=a\left(x-h\right)^2+k\)Part B
For the standard form, the vertex is given by
\(Vertex=(-b/2a,f\left(-b/2a\right))\)For the factored form, the vertex is given by;
\(Vertex=\left(\frac{p+q}{2},f(\frac{p+q}{2})\right)\)For the vertex form
\(Vertex=(h,k)\)Part C
For the standard form, the axis of symmetry is given by
\(x=-\frac{b}{2a}\)For the vertex form. the axis of symmetry is given by
\(x=h\)For the factored form, the axis of symmetry is
\(x=\frac{p+q}{2}\)Part C
I prefer the factored form because we can determine end behavior using the value of "a." Although the degree is not as easily identifiable, we know there are only two factors, making the degree two.
Also, we can easily identify the zeros or x-intercepts of the function. This is given by the values of p and q.
Lastly, we can easily get the vertex using the formula denoted above.
Only the factored form easily offers the three possiblities written above.
Related Questions
How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?
Answers
Answer:
To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.
First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.
Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.
Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.
However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.
A triangle has an area of 114.6 square kilometers and a height of 12 kilometers. What is the length of the base?
Answers
Answer:
base = 19.1 km
Step-by-step explanation:
start with formula:
A = bh/2
plug in what's known:
114.6 = 12b/2
114.6 = 6b
b = 114.6/6
b = 19.1
Hi can any one teach me this constant difference
Answers
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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You need 1 1/4 cups of sugar to make 20 cookies.
How many cups of sugar will you need to make 16 cookies?
Answers
Only 1 cup of sugar will be required to make 16 cookies
As mentioned in the question to make 20 cookies requires 1 1/4 cups of sugar. In order to make 16 cookies the amount of sugar required in the process would be less.
Thus, we can conclude that there exists a direct proportion between the amount of sugar and cookies required to make.
Let us take the amount of sugar required to make 16 cookies as x.
Thus, by applying the unitary method
x = 5/4 × 16/20 (1 1/4 = 5/4)
x = 1
∴ 1 cup of sugar is required to make 16 cookies.
Derive the positive square root of 982081
Answers
Answer: 991
square root of 982081 hope this helps
A quarterback completes 44% of his passes. Show all work.
a. Construct a probability distribution table (out to n = 6) for the number of passes attempted before the quarterback has a completion?
b. What is the probability that the quarterback throws 3 incomplete passes before he has a completion?
c. How many passes can the quarterback expect to throw before he completes a pass?
d. Determine the probability that it takes more than 5 attempts before he completes a pass.
e. If he throws 8 passes on the opening drive, what is the probability that he made at least half of them?
Answers
a.The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. the probability is 0.1399.
c. the quarterback can expect to throw about 2.27 passes before completing one.
d. the probability is 0.1865.
e. the probability is 0.7349.
what is probability?The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.
a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:
P(X=k) = \((1-p)^{k-1}\)×p
where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.
The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:
P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰
= 0.56²×0.44
= 0.1399
Therefore, the probability is 0.1399.
c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:
E(X) = 1/p
where p is the probability of completion on each attempt.
In this case, p = 0.44, so the expected number of passes is:
E(X) = 1/0.44
= 2.27
Therefore, the quarterback can expect to throw about 2.27 passes before completing one.
d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:
P(X > 5) = 1 - P(X <= 5)
= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]
= 0.1865
Therefore, the probability is 0.1865.
e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:
P(X ≥ 4) = 1 - P(X < 4)
where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.
Using the binomial probability distribution table or calculator, we can find:
P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]
= 0.7349
Therefore, the probability is 0.7349.
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-4=2/3 b
What would be the best first step to solving the
equation in one step
Answers
what is -7 + 3x = 8 - 2x
Answers
Answer: x = 3
Step-by-step explanation: -7 + 9 = 8 - 6
Help plssss ASAP!!!!!
Answers
Answer: D
Step-by-step explanation: You just have to substitute the numbers for the variable in each equation till you get the right one. Sorry, but I don't remember the formula for it.
why is 5.1 bigger than 5.099
Answers
5.1 is greater than 5.099, because the value of the 1 in 5.1 is more than the value of the 99 in 5.099.
\(\begin{gathered} 5.1=5+0.1=5+\frac{1}{10}=5+\frac{100}{1000} \\ 5.099=5+0.099=5+\frac{99}{1000} \end{gathered}\)The value of 1 in 5.1 is 0.1, while the value of the 99 in 5.099 is 0.099.
Since 0.1 is bigger than 0.099, then 5.1 is bigger than 5.099.
Also, 5.1 is greater than 5.099 because a bigger number on 5.1 (which is 1) is closer to the decimal point compared to 5.099 (1 is bigger than 0). the closer a decimal is to the decimal point the higher its value.
Read the following statement:
If m∠A = m∠B, then m∠B = m∠A.
This statement demonstrates:
the transitive property of equality.
the reflexive property of equality.
the symmetric property of equality.
Answers
This is the symmetric property of equality.
Its saying that if something is equal to something else, that other thing is equal to the other thing.
Basically, heres an example.
2 = 2
2 = 2
I flipped them, did you notice? The numbers are the same. It doesn't matter which side of the equals sign things go on.
Same thing for angles.
If angle A = angle B, then angle B = angle A.
If you were say say angle A was 45 degrees, then angle B must be 45 degrees too.
45 = 45
45 = 45
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
july 15, 2017 + 7months
Answers
Answer:
February 15, 2018
Step-by-step explanation:
Not sure but I think
The product of three integers is −11. Determine all of the possible values for the three factors. Write each set of three factors in order from least to greatest. Make sure that each set uses unique integers. Listing the sets in a different order doesn't count.
Answers
Answer:
(-1, 1, 11), (-11, -1, -1), (-11, 1, 1)
Step-by-step explanation:
An integer is basically a whole number that can either be be zero, positive or negative.
Now, we are told that the product of three integers is −11.
The factors of 11 are 1 and 11
Thus;
The possible set of three factors that can give a product of -11 are;
(-1, 1, 11), (-11, -1, -1), (-11, 1, 1)
The coordinates of point A on a grid are (−2, −4). Point A is reflected across the y-axis to obtain point B. The coordinates of point B are (, −4).
Answers
The coordinates of the point B are given as (2, - 4)
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Under a reflection in the y- axis
A point (x, y) → (- x, y), hence
A(- 2, - 4) → B(2, - 4)
Therefore the coordinates of the point B are given as (2, - 4)
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Solve the proportion.
w 100
88
3
a.
1
b. 9
A
B
C. 8
d.
Please select the best answer from the choices provided
OD
000
Answers
C. 8
8/3 = g/3
, x3 both side
8/3 x 3 = g
8/3 x 3/1 = g
24/ 3 = g
8 = g
Hope this helps!
in your own words, describe how to plot or graph an ordered pair of numbers.
Answers
Identify the two numbers in the ordered pair, locate the x-axis and y-axis on the plane, move along the x-axis to the position corresponding to the first number, move vertically along the y-axis to the position corresponding to the second number, mark the point with a dot or small circle, and connect the dots to show patterns.
How to plot or graph an ordered pair of numbers?The procedures below must be followed in order to plot or graph an ordered pair of integers, usually known as a point, on a two-dimensional plane:
Find the two numbers that make up the ordered pair. The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.On the plane, find the x- and y-axes. The y-axis is the vertical axis that runs up and down, and the x-axis is the horizontal axis that travels left to right.Move along the x-axis to the location corresponding to the first number in the ordered pair starting from the origin, which is the location where the x-axis and y-axis intersect (often represented by the coordinates (0, 0)).Move up the y-axis vertically until you are in the position that corresponds to the second number in the ordered pair.The position of the ordered pair on the two-dimensional plane is determined by the intersection of the two lines.Make a little circle or a dot to symbolize the point on the graph.If you need to plot more than one point, follow the instructions above for each additional point, identifying each one with a different symbol or color.To demonstrate any patterns or trends in the data, finish by connecting the dots.To know more about graph, visit
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need help real baddddddddddddd
Answers
Answer:
x≥2 and x<2 : ∅
x≥2 or x<2 : All real numbers
x≤2 and x≥2 : 2
Step-by-step explanation:
the first one must follow both conditions, so no number would work.
the second one works with any number, so all real numbers.
the third one has only one condition that works, 2
Suppose I rolled a fair six-sided die. Let R=number rolled. What is the sample space,
what is the expected value?
Answers
Answer:
No Side Is Being Favored Since The Die Is A Fair Six-Sided Die.
So Each Number Has The Same Chance Of Being Rolled.
EC - The ratio of three numbers is 2:7:1.
The sum of the numbers is 30. What are the
three numbers?
Answers
Answer: 6, 21, 3
Step-by-step explanation:
2:7:1
Also, 2x 7x and 1x or just x
2x+7x+x = 30
10x = 30
x=3
So the three numbers: 2(3):7(3):1(3) OR 6:21:3
Learning Task 3 Answer the questions that follow. Put a check mark (/) on the space provided. Copy and answer in your math notebook. 1. The units for Volume are always ______squared _____cubed 2. Volume is the amount of space an object takes up. ___True ___False Calculate for the volume of solid. 3. Chona is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 4. A 3-tier cake with the same height of 10 in and radius of 12 in, 8 in, 5 in respectively is to be delivered to a birthday party. How much space does this cake take up? Use 3.14 for π. 5. A Styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for π.
Answers
3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.
4. The cake takes up approximately 7317 cubic inches of space.
5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.
1. The units for Volume are always cubed.
2. Volume is the amount of space an object takes up. True.
3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:
V = 3.14 * (4.5)^2 * 32
V = 3.14 * 20.25 * 32
V ≈ 2034.72 cubic inches
4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.
Tier 1:
V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches
Tier 2:
V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches
Tier 3:
V3 = 3.14 * (5)^2 * 10 = 785 cubic inches
Total volume:
Total V = V1 + V2 + V3
Total V = 4521.6 + 2010.4 + 785
Total V ≈ 7317 cubic inches
5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:
V = (1/3) * 3.14 * (24)^2 * 12
V = (1/3) * 3.14 * 576 * 12
V ≈ 7234.08 cubic centimeters
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How much bigger is the 5 in 35.76 than the 5 in 26.95
Answers
The five in 35.76 is 100 times bigger than the five in 26.95.
How to compare the place values?Here we want to compare the values of the 5's in two different numbers, which are 35.76 and 26.95.
To compare them we need to compare the place value in which each five is.
To compare them, just write the numbers but replacing all the other values by zeros:
35.76 = 05.00 = 5
26.95 = 00.05 = 0.05
Now take the quotient of these two, we will get:
5/0.05 = 100
Thus, the 5 in 35.76 is 100 times bigger than the 5 in 26.95.
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Deymarius drank 2/3 of a quart of water. Wesley drank 1/6 of a quart of water. how many quarts of water did they drink all together?
Answers
Answer:
5/6 quarts of water
Step-by-step explanation:
2/3 same as 4/6. 4/6 + 1/6 = 5/6
How do I solve 4x^2+6x=0 by factoring
Answers
Answer: \(x=0, -\frac{3}{2}\)
Step-by-step explanation:
\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)
The ratio of the sides of rectangle LMNP to the sides of rectangle TUVW is 1:4. The length of LM is 3.6 in, and the length of UV is 16 in.
What is the difference between the areas of the two rectangles?
A. 226 in2
B. 172.8 in2
C. 211 in2
D. 216 in2
Answers
A scale model of a ramp is a right triangular prism as given in this
figure. In the actual ramp, the triangular base has a height of 1.2
feet.
What is the surface area of the actual ramp, including the
underside?
Enter your answer as a decimal in the box.
ft?
Answers
The surface area of the prism is 16.8 ft²
What is scaling?
Scaling is the increase or decrease in the size of a figure.
The scale = 1.2 feet / 6 cm = 0.2 ft/cm
9 cm = 0.2 ft/cm * 9 cm = 1.8 ft, 10 cm = 0.2 ft/cm * 10 cm = 2 ft, 16 cm = 0.2 ft/cm * 16 cm = 3.2 ft,
Surface area = 2(0.5 * 3.2 * 1.2) + 2(1.8 * 2) + (1.8 * 3.2) = 16.8 ft²
The surface area of the prism is 16.8 ft²
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LetA=(3,2),B=(1,5),andP=(x,y).Find x-and y-values that make ABP a right angle.
Answers
Answer:
Step-by-step explanation:
Without a picture reference that would exclude certain points there are 6 possible right triangles that can be formed by adding points
(-1,2), (1,-1), (1,2), (3,5), (3,7), (5,5)
could someone help me with this and show work?
Answers
The volume of the shape is 490cm³
What is volume of prisms?A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.
The base of this prism is rectangular. The volume of a prism is expressed as;
V = base area × height
base area = 7 × 10 = 70cm²
height = 7cm
the volume of the shape = 70× 7 = 490cm²
therefore the volume of the shape is 490cm³.
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A pump moves 42 gallons in 7 minutes. How many gallons can the pump move per minute?
Answers
Answer:
6 gallons per minute
Step-by-step explanation:
42÷7= 6
Answer:
6 gallons per minute
Step-by-step explanation:
42/7=6
the radius of a circle is 3 inches. What is the lenght of a 180° arc?
Answers
The length of the 180° arc as required in the task content is; 22/21 inches.
What is the measure of the 180° arc's length?Recall that the length of an arc is given by the formula;
Length of arc = theta / 360 × 2 π r
Therefore, for a radius of 3 inches;
Length of arc = 180/360 × 2 × 22/7 × 3
Length of arc = 22/21 inches.
Ultimately, the length of the arc in discuss is; 22/21 inches.
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Please i need the answer fast k12
Answers
(A) The range and IQR for boxplot 1 is 10 and 6 respectively.
(B) The range and IQR for boxplot 2 is 12 and 7 respectively.
What is the IQR?The interquartile range defines the difference between the third and the first quartile.
The formula for the interquartile range is given below.
Interquartile range = Upper Quartile – Lower Quartile = Q3 – Q1
What is the range?The range is the difference between the lowest and highest values.
The formula for the interquartile range is given below.
Range = Maximum – Minimum
(A) For boxplot 1, we need to find the range and IQR from the given data set.
So, let 34 be the maximum and 24 be the minimum.
\(\text{Range}=\sf 34-24\)
\(\text{Range}=\sf10\)
Therefore, the range is 10.
Now time to find the IQR.
So, let 33 be Q3 and 27 be Q1.
\(\text{IQR}=\sf 33-27\)
\(\text{IQR}=\sf 6\)
Therefore, the IQR is 6.
(B) Now for boxplot 2, we will do the same thing as from part A.
Let's find the range.
So, let 24 be the maximum and 12 be the minimum.
\(\text{Range}=\sf 24-12\)
\(\text{Range}=\sf12\)
Hence, the range is 12.
Now for the IQR.
So, let 22 be Q3 and 15 be Q1.
\(\text{IQR}=\sf 22-15\)
\(\text{IQR}=\sf 7\)
Hence, the IQR is 7.
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