here is a sketch of y=x^2 + bx + c. the curve intersects the x-axis at (2,0) and point P. the y-axis at (0,14) work out the x-coordinate of the turning point of the graph
Answers
Finding the x-coordinate of the turning point of a quadratic equation requires knowledge of its coefficients. Given a function y = x^2 + bx + c, and points (2,0) and (0,14), we need further calculations or information to precisely identify b to use the vertex formula -b/2a effectively.
Explanation:To find the x-coordinate of the turning point of the graph of the quadratic equation y = x^2 + bx + c, we can use the fact that the vertex of a parabola given by the general form ax^2 + bx + c is at x = -b/2a. Since the quadratic intersects the x-axis at (2,0), we can plug x = 2 into the equation to find one relation between b and c.
Another given point is (0,14), which when plugged in gives c = 14. To find b, we need more information from the question or an understanding of quadratic functions more deeply. However, without b, we can use the vertex formula derivatively, knowing that a in our equation is 1 (since the coefficient of x^2 is 1).
We also know that for any quadratic function, the x-coordinate of the vertex (turning point) can be found using -b/2a. Without the exact value of b, we cannot find the exact x-coordinate directly from the information given.
However, the general methodology would involve using the known points to first find equation coefficients and then apply the vertex formula. This highlights the importance of understanding quadratic functions and their graphical representations, such as vertices and intercepts, to solve these types of problems efficiently.
The x-coordinate of the turning point of the graph is 4.5
How to determine the x-coordinate of the turning point of the graph
From the question, we have the following parameters that can be used in our computation:
[tex]y = x^2 + bx + c[/tex]
It intersects the y-axis at (0, 14)
This means that
[tex]0^2 + b(0) + c = 14[/tex]
c = 14
So, we have
[tex]y = x^2 + bx + 14[/tex]
It intersects the x-axis at (2, 0)
So, we have
[tex]2^2 + 2b + 14 = 0[/tex]
4 + 2b + 14 = 0
2b = -18
b = -9
So, we have
[tex]y = x^2 - 9x + 14[/tex]
The x-coordinate of the turning point of the graph is then calculated as
x = -b/2a
So, we have
x = 9/2
x = 4.5
Hence, the x-coordinate of the turning point of the graph is 4.5
Related Questions
The function f(x) =g(x), where f(x) =2x-3 and g(x) =x^2-5
Answers
Answer:
x=2.732
Step-by-step explanation:
Given are two functions
f(x) = 2x-3 and g(x) = [tex]x^2-5[/tex]
WE have to find the approximae value when these two funcitons are equal
Since we are asked to find only positive value we can refer table and do
f(2) >g(2) but f(3)<g(3) Hence there is one solution between 2 and 3.
f(2.5)>g(2.5). So the root lies between 2.5 and 3 since change of sign takes place here
x f g
2.6 2.2 1.76
2.7 2.4 2.229
2.72 2.44 2.398
2.73 2.46 2,453
2.732 2,464 2.464
Hence answer is x =2,732
Translate this sentence into an equality
the quotient of x and 7 is at most -24
Answers
x ÷ 7 ≤ -24
↑
This symbol is there because x ÷ 7 cannot be more than -24, but can be less than or equal to -24.
Hope this helps!
Jorge bought a crate of floor tiles for 95.94. The crate had 6 boxes of floor tiles. Each box contained 20 floor tiles
Write and solve an equation to determine the cost per box, b. Then write and solve a second equation to determine the cost per tile, t, the nearest cent
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then to find the cost per tile it would be 15.9 divided by 20 = t or 78 cents per tile
Answer:
Step-by-step explanation:
6b= 95.94 divide will give you $15.99 then divide 20 into 15.99 will give you .7995 they said nearest cent.
i need the answer as soon as possible :)
A $12,500 loan for 3 years, compounded at an annual interest rate of 18%.
Find the total amount owed.
A) $21,157.90
B) $13,187.22
C) $8,037.90
D) $20,537.90
Answers
The distance between two towns is 12 5/8 miles. Mr.Lang has driven 4 5/12 miles of distance. How much farther does he have left to go?
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[tex]\sf 12\dfrac{5}{8}-4\dfrac{5}{12}[/tex]
Convert them to improper fractions. We do this by multiplying the denominator to the whole number, adding it to the numerator, which becomes the numerator, and we keep the denominator the same.
[tex]\sf\dfrac{101}{8}-\dfrac{53}{12}[/tex]
To subtract fractions we need a common denominator. The least common multiple of 8 and 12 is 24. Convert both fractions to denominators of 24, find out how many times the current denominator goes into 24, then multiply that number to both the numerator and denominator:
[tex]\sf\dfrac{303}{24}-\dfrac{106}{24}[/tex]
Now we can subtract the numerators and keep the denominator the same:
[tex]\sf\dfrac{197}{24}[/tex]
Convert back to a mixed number. Twenty-four goes into 197 eight times. 24 * 8 = 192. 197 - 192 = 5. So we have 8 whole 24s and 5/24 left, or:
[tex]\boxed{\sf 8\dfrac{5}{24}}[/tex]
An isosceles trapezoid has a perimeter of 57 millimeters. Its shorter base measures 6 millimeters and its longer base measures 15 millimeters. The two remaining sides have the same length; what is that length?
Answers
If we subtract from the perimeter the lengths of the two bases, we end up with the combined length of the two legs. Since the legs are congruent, we divide the combined length of the two legs by 2 to find the length of each leg.
perimeter - base - base = combined length of legs
57 mm - 6 mm - 15 mm = 36 mm = combined length of legs
36 mm / 2 = 18 mm = length of each leg
Answer: the length of each leg is 18 mm.
Simplify fully the square root of 1/169
Answers
The fully simplified form of √(1/169) is 1/13.
Given that an expression √(1/169), we need to simplify it,
To simplify the square root of 1/169, we can break it down as follows:
√(1/169)
Since 1 is the square of itself (1² = 1), we can rewrite the expression as:
√(1/169) = √(1)/√(169)
The square root of 1 is simply 1:
√(1/169) = 1/√(169)
Now, the square root of 169 is 13:
√(1/169) = 1/13
Therefore, the fully simplified form of √(1/169) is 1/13.
Learn more about square root click;
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A 20ft ladder leans against a house. The bottom of the ladder is 8 feet from the base of the house. To the nearest foot, how high above the ground is the top of the ladder?
Answers
[tex] {8}^{2} \times {x}^{2} = {20}^{2} [/tex]
then solve for x to find the height
Should come out to be around 18 feet
What is the value represented by the letter A on the box plot of the data?
{10, 12, 15, 21, 24, 30}
Enter your answer in the box.
Answers
the part furthest to the left always represents the least number.
:)
The value of letter A on the box plot is given by A = 10
What is box plot?A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.
here, we have,
we know that,
A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.
It is used when showing the distribution of data points across a selected measure and if the box in a box plot is stretched in one direction or the other, then the data is skewed in that direction.
Given data ,
Let the box plot be represented as Z
Now , the values of the data from the box plot is given by
Z = { 10 , 12 , 15 , 21 , 24 , 30 }
The value of the letter A from the box plot is the first value
where A = 10
Therefore , the value of A is 10
Hence , the box plot is solved
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Use the steps to solve the Carbon Dating Problem.
1. Graph the function C(t) = 100•e^-0.000121t using points (t, C(t)).
Answers
Use what you learned in the lesson and the online content to answer the following question: Which renewable source of energy should the United States focus its research and development efforts to make this source of energy our country’s main energy source by the year 2050? Why?
Answers
Answer:
Renewable electricity
Step-by-step explanation:
Renewable electricity is an option for everybody. Using a small solar panel device can create renewable electricity for your home. Renewable electricity is safer and cleaner.
The renewable source of energy is the generation of energy from naturally extracted resources. These sources are naturally replenishing due to excess consumption and overpopulation.
These renewable sources are virtually inexhaustible. The types of renewable energy sources are: biodiesel, wind, solar, hydropower, and many more.
Renewable electricity is the source of energy upon which the United States must focus its research and development efforts.
Renewable electricity is the most suitable option over which the research and development must focus for making it one of the main sources of energy for the country by the yer 2050.
This can be done by using solar panel devices at homes and factories so that they can generate their own electricity. This will help in saving the electricity supply from the poles.
To know more about renewable energy, refer to the link:
https://brainly.com/question/4038933
The quotient of m and 7
Answers
Each of these circles represents a pizza cut into 10 equal slices, and the yellow slices are the ones eaten by Larry.
If Larry ate L% of the total amount of pizzas, what is the value of L?
Answers
Answer:
Where is the pic?
the equation of a circle is (x-5)^2+(y+3)^2=25 what are the coordinates of the center of this circle
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Notice that in the equation, we have [tex]-h[/tex] and [tex]-k[/tex]. When writing the ordered pair alone, we have to remember to flip the sign.
Therefore, we have [tex](5, -3)[/tex].
what are the whole numbers between 2 and 8
Answers
Let me lay this out for you the best I can.
2. 3. 4. 5. 6. 7. 8
In between the numbers 2 and 8, there are 5 numbers, which are 3,4,5,6, and 7.
how too solve for x 5x+8
Answers
I'm pretty sure that is as simplified as it can be
Kerrie cover a table with 8 rows of square tiles there are 7 tiles in each row what is the area the Kerrie covers in square units?
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Kerrie covered a table having 8 rows of square tiles.
Each row has 7 tiles. The table will be rectangular in shape.
The number of rows will be the length of the table and the number of tiles in each row will be the width of the table.
Area of rectangle = length x width.
Area of the table = 8x7= 56 square units.
The area covered by Kerrie is [tex] 56unit ^{2} [/tex]
Find two consecutive whole numbers that square root 62 lies between
Answers
The square root of 62 lies between the consecutive whole numbers 7 and 8, because 7² is 49 and 8² is 64, and 62 is between these two square numbers.
Explanation:The student is asking for two consecutive whole numbers between which the square root of 62 lies. First, identify the whole numbers whose square roots are immediately less than and greater than √62. Considering square numbers we know, 7² = 49 and 8² = 64. Since 49 < 62 < 64, the square root of 62 must be between 7 and 8. Therefore, the two consecutive whole numbers are 7 and 8, as √62 is greater than 7 but less than 8.
y=x^2-16x+63
[tex]y = x { }^{2} - 16x + 63 \\ [/tex]
Answers
[tex]given \: expression \: - \\ \\ y = {x}^{2} - 16x + 63 \\ \\ y = {x}^{2} - 7x - 9x + 63 \\ \\ y = x(x - 7) - 9(x - 7) \\ \\ y = (x - 9)(x - 7) \: \: \: \: \: \: ans. \\ \\ \\ additional \: calculation \: - \\ \\ had \: been \: \: y = 0 \\ \\ we \: would \: have \: got \: \\ x = 9 \: \: \: \: \: or \: \: \: \: \: x = 7[/tex]
The equation provided is a quadratic equation in standard form, which can be solved using methods such as factoring, completing the square, or the quadratic formula to find its roots.
Explanation:The equation y=x^2-16x+63 is a quadratic equation, which is a polynomial equation of the second degree. The standard form of a quadratic equation is ax^2 + bx + c = 0. To solve this equation for x, you can either factor it, complete the square, or use the quadratic formula. If this specific equation was meant to be solved, we would look for values of x that make the equation true. This involves finding the roots of the equation, which are the x-intercepts of the parabola represented by the equation on a graph.
Which steps should be followed to use a scale drawing and a new scale to find the new length of a soccer field? Add the numerator of the new scale to the old length to get the new length. Subtract the new length from the old length to find the difference in lengths. Write a proportion using the new scale as the first ratio. Set the first ratio equal to the ratio of the length of the original field compared to a variable that represents the new length of the field. Solve the proportion to find the new length of the field. Write a ratio comparing the scale drawing length to the actual length of the field, and simplify.
Answers
Solving proportions with a missing variable always involves setting the proportions equal to each other, and then solving for the missing variable.
I have the same values as a group of 2 dimes and 1 nickel what coin am I
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A dime = 10
So 2 dimes would equal 20 cents.
A nickel= 5 cents
20+5= 25
25 cents equals a quarter
So a quarter is ur answer!!
Hope this helps
Write the statement for the problem in mathematical language. Use x for the tens digit and y for the unit digits in the two digit numbers. Find the two-digit number which is greater than the product of its digits by 26
Answers
_____
This can be rearranged to
.. y = 10 -16/(x -1)
so x-1 must be a factor of 16 that is larger than 1, hence 2, 4, 8.
Integer solutions are (x, y) = (3, 2), (5, 6), (9, 8).
PLEASE HELP ASAP!!!!!!!!!
Answers
B.(5,5)
C.(7,3)
D.(5,2)
Can someone help meh. Trying to reach Ace tank.
what is the surface area of this triangular prism
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length =3 cm
Side =10 cm
Height = 8cm
A=bh+2ls+lb
A= 192cm is surface area. hope this loves.
Which statement is NOT true?
F. A set of ordered pairs that describes a function cannot have any y-value repeated.
G. A table of values describes a function if all the x-values are different.
H. A mapping is a function if each x-value is paired with exactly one y-value.
J. A graph describes a function if no point on the graph lies directly above or below another of the graph.
Answers
~~
Why??
F - it can be a function even if a y - value repeats itself its the x - values that cannot repeat in order to be a function.
G - this is true as stated above.
H - a mapping is a function if each x - value is paired with only one y - value. If an x - value was paired with multiple y - values then its the same thing as repeated x - values.
J - this is true. To check if a graph is a function try the vertical line test. Simply take a ruler holding it vertically ( up and down ) and place it over a point on the graph. If there is another point lined up with the first one ( above or below ), then it is NOT a function.
~~
I hope that helps you out!!
Any more questions, please feel free to ask me and I will gladly help you out!!
~Zoey
Screenshot included! MY LAST QUESTION! What is the volume of this aquarium?
96 in³
2,304 in³
3,216 in³
4,608 in³
Answers
The front of an a-frame house is in the shape of a triangle.The height of the house is 20 feet.The area of the front of the a-frame is 600 square feet.Write and solve an equation to find the base of the A-frame house
Answers
[tex] \frac{1}{2} *b*h[/tex]
Where:
- b is the base length
- h is the height
So, basically just plug things in:
Answer:
60 feet
Step-by-step explanation:
Multiply the area by 2 to get 1200 feet. then, divide by 20 to get 60. The base of the a-frame is 60 feet.
What’s the nth term of 40 35 30 35 20
Answers
where n is the number, you always take away 5 and you add 45 because that is the first number of the sequence
What is the surface area of the cube with the rectangular prism
155 in
270 in
300 in
310 in
Answers
help me please I dont know the answer..
Answers
X= -1
Y=-8
Hope this help
For this case what you should do is see the intersections with each of the axes and then join the ordered pairs.
We have then:
For the x axis:
y = 0
Substituting in the equation:
8x + (0) = - 8
8x = -8
x = -1
For the y axis:
x = 0
Substituting in the equation:
8 (0) + y = -8
0 + y = -8
y = -8
We graph the ordered pairs:
(x1, y1) = (- 1, 0)
(x2, y2) = (0, -8)
Answer:
See attached graph.