Use the parabola tool to graph the quadratic function. f(x)=2x2+12x+16
Answers
f(x)=2x²+12x+16
using a graph tool
see the attached figure
Answer:
Step-by-step explanation:
To obtain the graph of a parabola, three data are necessary: the vertex (the vertex is the highest or lowest point of the graph corresponding to the parabola and there it is on the plane of symmetry of the parabola), the roots ( those values of x for which the expression is 0. Graphically, the roots correspond to the abscissa of the points where the parabola cuts the x-axis.) and the concavity.
Being f(x)=ax²+bx+c, you can see that, in this case, a=2, b=12 and c=16. So:
Vertex= for your calculation, [tex]xv=\frac{-b}{2*a}=\frac{-12}{2*2}[/tex], so xv=-3. Now that you know x, all you have to do is enter its numerical value into the original formula to find yv. yv=2*(-3)²+12*(-3)+16. Then yv=-2Roots: The roots are calculated using the expression: [tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]. Replacing the values that you have:[tex]x1,x2=\frac{-12+-\sqrt{12^{2}-4*2*16 } }{2*2}[/tex] Solving, you obtain x1=-2 and x2=-4Concavity: If a> 0 (positive) the parabola is concave or pointed upwards, while if a <0 (negative) the parabola is convex or pointed downwards. In this case a = 2, so the parabola opens upward, being concave.In this way, the graph shown in the attached image is obtained.
Related Questions
Determine whether the following expressions are equivalent to 3(4+2b) . Expressions Yes - Yes No - No 24b 6(b+2) (12b+2b) 6b+12
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6(b+2)
This would help :))
What’s 5/9 rounded to the nearest half
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Hope this helped☺☺
The round off to nearest half is 1/2.
What is Round off?Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
The fraction = 5/9.
Now, rounded to the nearest half is 1/2
we know 9 halved value is 4.5 which is much closer to 5.
So, we can write it as 5/10 = 1/2.
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Four friends share 3 apples equally. what fraction of an apple does each friend get
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This would be 1/4 * 3, or 3/4 of an apple.
What is the slope of the line that passes through the points (2, 3) and (–2, 6)?
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What is the slope of the line passing through the point (-3,-1) and the origin?
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Which explanation justifies how the area of a sector of a circle is derived?
- Determine how many triangles can fit into a circle. Divide 360° by the number of triangles. Multiply the quotient by the area of the circle .
- Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.
- Partition the circle into unit squares. Determine the area of the sector and multiply the area by the degree of the circle.
- Determine the degree of the sector. Divide by 180° and then multiply it by the area of the triangle the sector is in.
Answers
hope it helps!!
The statement that justifies how the area of a sector of a circle is derived is:
Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.What is an area?This refers to the quantity that expresses the extent of a region on the plane such as on a curved surface.
Furthermore, the area of sector of a circle is talking about the amount of space enclosed within the boundary of the sector.
Generally, it is explained in step that we first calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.
Therefore, the Option B is correct.
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What is the following product? 4 square root 7
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"4√7" means four times the square root of 7, approximately equal to 10.582, an irrational number with decimal expansion.
The expression "4√7" represents the square root of 7, multiplied by 4. Let's break it down step by step:
1. Square Root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Similarly, the square root of 25 is 5 because 5 × 5 = 25.
2. √7: This symbol (√), called the radical symbol, represents the square root. So, √7 represents the square root of 7, which is an irrational number, meaning it cannot be expressed as a simple fraction and has decimal places that go on indefinitely without repeating.
3. 4√7: This means you're taking the square root of 7 and then multiplying it by 4. So, if you calculate it, it's like doing 4 times the square root of 7.
To give a numerical example, if we want to find the value of 4√7:
4 × √7 ≈ 4 × 2.6457513110645905905016157536393... (approximately)
Thus, 4√7 is approximately equal to 10.582, depending on how many decimal places you round to.
In summary, "4√7" represents four times the square root of 7, which is an irrational number, approximately equal to 10.582.
You charged $65 dollars on a credit card and you returned a item hat was pitched with the card and it cost $24? Then u bought an item with he card that cost $24 dollars
Answers
Use 3.14 for and round your final answer
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4/3 x 3.14 x 8 ^{3}
4/3 x 3.14 x 512
4/3 x 1607.68
2143.57 (I also got 2144.66 if the first one doesn't work)
what was sal finding when he plugged t=10 into the expression 5t+3?
a. The cost of 10 tickets
b. The cost of 53 tickets
c. The number of tickets that would cost 10 dollars
d. The number of tickets that would cost 53 dollars
Answers
Answer:
a. The cost of 10 tickets
Step-by-step explanation:
We don't know what the expression is supposed represent, but the answer choices suggest that ...
c = 5t +3
represents the cost of t tickets. Then, when t=10, c = 53 will represent the cost of 10 tickets.
An Investor invested a total of $2,600 in two mutual funds. One fund earned 7% profit while the other earned 3% profit. If the investor’s total profit was $150, how much was invested in each mutual fund?
Answers
let x = amount invested at 3%
so, (2600 - x) is invested at 7%
.07 *(2600 - x) + .03 *(x) = 138
182 - .07x + .03x = 138
-.07x + .03x = 138 - 182
-.04x = -44
-.04x / -.04 = -44 / -.04
x = 1,100
so amount invested at 7% is (2600 - 1100) or 1500
consequently amount invested at 3% is 1100
$1,100 invested at 3%
$1,500 invested at 7%
The money invested in both of the funds are $800 and $1800 respectively.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Suppose the money invested in one of the funds be x.
Then, in the other fund the investment is (2600 - x).
Now, the equation for the total profit from both investments can be obtained as,
7% × x + 3% × (2600 - x) = 150
⇒ 7/100 × x + 3/100 × (2600 - x) = 150
⇒ 4x/100 = 150 - 78
⇒ x = 1800
Thus, the investment in the other fund is 2600 - 800 = $800.
Hence, the investment for both the funds are $800 and $1800 respectively.
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Please help me with these!!!
Simplify these expressions:
a) 3 2/3x-4/5(x- 3 3/4)
b) 2 1/4x+(4 1/3x-7 4/5) divided by 2 3/5
c) 8x-1 1/7 (1 1/3x-12)
d) 11 4/7x+(5x- 2 2/5)
Answers
Answer:
A) 2 13/15 x + 3
B) 2 7/12 x - 7 4/5 over 2 3/5
C) 5 16/21 x - 18 6/7
D) 16 4/7 x - 2 2/5
Step-by-step explanation:
There are 56 trees in an apple orchard. They are arranged in equal rows. There are 8 trees in each row. How many rows of apple trees are there? Which equation can be used to solve this problem?
Answers
56 divided by 8 is 7
Hope this helped :)
Which ratio can be used to convert meters to kilometers
Answers
We can use the ratio of 1000meters=1km
So if we have say 100meters and want this unknown we simply take
100m/1*1m/1000km=0.100km
We can also think of meters and kilometers in powers of ten.
1m=1.00*10^-3km=0.001km
Hope this helps some! Any questions please just ask! Thank you!!
Rewrite the following equation in slope-intercept form. 10x − 17y = -12 Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
y = (10/17) x + (12/17)
Explanation:
The slope-intercept form has the following formula:
y = mx + c
where:
m is the slope
c is the y-intercept
The given is:
10x - 17y = -12
To put this in slope-intercept form, we need to isolate the y as follows:
10x - 17y = -12
17y = 10x + 12
y = (10/17) x + (12/17)
where:
m is the slope = 10/17
c is the y-intercept = 12/17
Hope this helps :)
10x = -12
X = -12/10 = -6/5
X=0
-17y=-12
Y= 12/17
2 × 7/8 as a model how do I draw it as a model
Answers
You can draw 8 tiles, and color in 7.
Draw that two times.
That’s one way, but that might not be the way you learned it.
Hope this helped anyways!
A rectangular prism is completely packed with 90 cubes of edge length 1/2 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism?
A: 11 unit cubes and 1 smaller cube of volume 1/8 cubic inch
B: 22 unit cubes and 4 smaller cubes of volume 1/8 cubic inch each
C: 11 unit cubes and 2 smaller cubes of volume 1/8 cubic inch each
D: 22 unit cubes and two smaller cubes of volume 1/8 cubic inch each
Answers
So we come up with the answer of letter C.
Answer:
C. (11 unit cubes and 2 smaller cubes of volume 1/8 cubic inch each.)
Step-by-step explanation:
90 cubes * 1/8 inch = 11 1/8 inch.
(Please help HURRY!) (Don't delete this!) (I WILL GIVE BRAINY!)
1. ABC undergoes a dilation, with a scale factor of 8, to form A'B'C'.
Side A'B' is 8 times the length of side AB.
What is the area of A'B'C', compared to the area of ABC?
A. The area of A'B'C' is 1/8 of the area of ABC
B. The area of A'B'C' is 1/64 of the area of ABC
C. The area of A'B'C' is 8 times the area of ABC
D. The area of A'B'C' is 64 times the area of ABC
2. DEF undergoes a dilation, with a scale factor of 4, to form D'E'F'.
Side D'E' is 8 times the length of side DE.
What is the area of D'E'F', compared to the area of DEF?
A. The area of D'E'F' is 1/4 of the area of DEF
B. The area of D'E'F' is 1/16 of the area of DEF
C. The area of D'E'F' is 4 times the area of DEF
D. The area of D'E'F' is 16 times the area of DEF
3. ABC undergoes a dilation, with a scale factor of 3, to form A'B'C'.
Side A'B' is 3 times the length of side AB.
What is the area of A'B'C', compared to the area of ABC?
A. The area of A'B'C' is 1/3 of the area of ABC
B. The area of A'B'C' is 1/9 of the area of ABC
C. The area of A'B'C' is 3 times the area of ABC
D. The area of A'B'C' is 9 times the area of ABC
Answers
2. C
3. I think B
area of triangle is = 1/2 * base * altitude
1- each side is made 8 times
so the net change in area is 64 times
The area of A'B'C' is 64 times the area of ABC
2- each side is made 4 times
so the net change in area is 16 times
The area of D'E'F' is 16 times the area of DEF
3- each side is made 3 times
so the net change in area is 9 times
The area of A'B'C' is 9 times the area of ABC
can someone help ?? please
Answers
solomon has read 1/3 of his book. He finishes the book by reading the same amount eat night for 5 nights what fraction of the book does he read each of the 5 nights?
Answers
Final answer:
Solomon has 2/3 of the book left to read. To finish it over 5 nights, he needs to read 2/15 of the book each night.
Explanation:
Solomon has read 1/3 of his book already. To finish the remaining 2/3 of the book in 5 nights, we need to calculate the fraction of the book he should read each night. Since he has to evenly distribute the remaining portion over 5 nights, we will divide 2/3 by 5.
Here's the calculation step-by-step:
First, represent the remaining part of the book as a fraction, which is 2/3.
To divide this fraction by 5, we multiply the denominator by 5. This gives us (2/3) × (1/5).
Multiplying these fractions, we get (2 × 1) / (3 × 5), which simplifies to 2/15.
Thus, Solomon reads 2/15 of the book each night for the next 5 nights.
Select the statement that best justifies the conclusion based on the given information. Conclusion: l1 and l 2 intersect only at point P. A line contains at least two points. Through any two different points, exactly one line exists. If two lines intersect, then their intersection is exactly one point. If two lines intersect, then exactly one plane contains both lines.
Answers
If two lines intersect, then their intersection is exactly one point
Explanation:
Let's take a look at the choices:
Choice A: A line contains at least two points.
The statement is true. However, it is not related to intersection between lines. Therefore, this choice is wrong
Choice B: Through any two different points, exactly one line exists
This postulate is true. However, it does not relate directly to the intersection between lines. Therefore, this choice is wrong
Choice C: If two lines intersect, then their intersection is exactly one point.
This statement is known as theorem 1-1. It describes the intersection between two lines.
Therefore, this statement is correct.
Choice D: If two lines intersect, then exactly one plane contains both lines.
The conclusion given is related to points created due to intersection between lines. This option is therefore excluded as it describes planes.
Hope this helps :)
Answer:
If two lines intersect, then their intersection is exactly one point.
Step-by-step explanation:
solve the compound inequality
Answers
You want x alone, so subtract 4 from each of the 3 parts.
[tex] -3 \le x + 4 \le 13 [/tex]
[tex] -3 - 4 \le x + 4 - 4 \le 13 - 4 [/tex]
[tex] -7 \le x \le 9 [/tex]
[tex] x \ge -7 [/tex] and [tex] x \le 9 [/tex]
Answer the manager one
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irrational number of 5
Answers
Hope this helped
~Melis
Which equals 2.2360679....
Find the distance between (6,-3) & (-1, 7) on the CCS
Answers
Answer:
9 or (5,4)
Step-by-step explanation:
Just subtract it on each side :)
Describe the differences between vertical and adjacent angles
Answers
and adjacent lines are 2 angles that have a common endpoint and common sides
Which equation will help you solve this problem?
A band performed at halftime during the football game.
There were 64 band members marching in 8 equal rows.
How many band members were in each row?
Answers
So the answer is that 8 members was in each row.
Answer:
There are 8 band members in each row
Step-by-step explanation:
Given : A band performed at halftime during the football game.
There were 64 band members marching in 8 equal rows.
To Find : How many band members were in each row?
Solution :
Let there are x members in each row .
Since there are 8 rows
So, no. of members in 8 rows = 8x
We are also given that there are 64 band members .
⇒[tex]8x=64[/tex]
⇒[tex]x= \frac{64}{8}[/tex]
⇒[tex]x= 8[/tex]
Thus there are 8 band members in each row
what is the sum of the finite arithmetic series ? 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)
Answers
Good luck :)
[tex]\text{Consider the sum of the finite arithmatic series}\\ \\ 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)\\ \\ \text{We know that the sum of the finite arithmatic series }\\ \\ a_1,a_2, a_3, ..., a_n \text{ is given by the formula}\\ \\ S_n=\frac{n}{2}\left ( a_1+a_n \right )\\ \\ \text{here in the given series, we can see that }a_1=7.6, \ a_n=-1.5 \text{ and}\\ \text{the number of terms is, }n=8. \text{ so using above formula, we get}[/tex]
[tex]S_8=\frac{8}{2}\left ( 7.6+(-1.5) \right )\\ \\ =4\left ( 7.6-1.5 \right )\\ \\ =4\left ( 6.1 \right )\\ \\ =24.4[/tex]
Hence the sum of the finite Arithmetic series is: 24.4
Solve: 3(20 + 5y) = - 30.
y = -10
y = - 18
y = 2
y = -6
Answers
The answer to your question would be
Y= -18
This is because 3x20 is 60
so then it would be 60 + 3x5y= -30
it has to be a negative number because 60 is greater than -30
then you would add the absolute values which would be 60+30=90
And divide that by 5 which is 18, but then you have to add back on the negative sign.
Audrey is buying a nee car for $32,998. She plans to make a down payment of $4,200. If she's to make a monthly payments of $525 for the next five years, what APT has she paid?
Answers
4,200+525(60)=
4,200+31,500=35,700