For a quadratic in standard form f (x) = ax² + bx +e with
vertex (h,k), determine the indicated values.
Answers
For a general quadratic equation, we want to find the equations for the vertex (h, k).
The values of the vertex are:
h = -b/(2*a) k = f(h) = b^2/(4a) - b^2/(2a) + cWe start with the general quadratic equation:
f(x) = a*x^2 + b*x + c
To find the x-value of the vertex (h in this case) we need to find the zero of the first derivate of f(x) (because the vertex is a minimum/maximum of the function).
We have:
f'(x) = 2*a*x + b
We solve:
f'(h) = 0 = 2*a*h + b
-b/(2*a) = h
So we just found the value of h.
To find the value of k, the y-value of the vertex, we need to evaluate the function in the x-value of the vertex, we will get:
k = f(h) = a*( -b/(2*a))^2 + b*( -b/(2*a)) + c
k = b^2/(4a) - b^2/(2a) + c
Then, concluding, we have:
h = -b/(2*a) k = f(h) = b^2/(4a) - b^2/(2a) + cIf you want to learn more, you can read:
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Related Questions
(8×1017)÷(2×103)Give your answer in standard form.
Answers
sry I have to write extra stuff to send the answers :)
Find the greatest common factor of the following numbers.
Answers
Paul mixes nuts worth $1.40 per pound with oats worth $1.70 per pound to get 30 pounds of trail mix worth $1.50 per pound. How many pounds of nuts and how many pounds of oats did he use?
Paul used pounds of nuts and pounds of oats.
Answers
The quantity of pounds of nuts and oats used by Paul is 20 and 10 pounds respectively.
According to the question:
Let pounds of nuts used = x Let pounds of oats used = yTotal quantity of trail mix used = 30 pounds and Overall cost of trail mix = 30 × 1.50 = $45.The information above can be used to generate two equations as follows;
1.4x + 1.7y = 45.............eqn(1)x + y = 30.......................eqn(2)Consequently, by solving the equations simultaneously; we have;
Pounds of nuts, x = 20 pounds.Pounds of oats, y = 10 pounds.Read more:
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I need help please!!!
Answers
Answer:
yes yes ok you need help mr
determine if the mapping diagram represents a function
Answers
Answer:
Yes, because each domain have only one range.
Step-by-step explanation:
Find the slope
Options
B.-1
C.1/4
D.4
Answers
Explanation:
Start at the point (-1,-4). In order to move to (0,0), we must do the following two steps:
Move 4 units upMove 1 unit to the rightThis indicates slope = rise/run = 4/1 = 4.
You could use the slope formula to get this same result.
3|5x+2|+10=4
Absolute value
Answers
So your answer is : no solution
Members of a softball team raised $1158.25 to go to a tournament. They rented a bus
for $836.50 and budgeted $24.75 per player for meals. Write and solve an equation
which can be used to determine p, the number of players the team can bring to the
tournament.
Equation:
Answer: p =
Submit Answer
attempt out of
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69°F
Answers
Answer:
1518.25=836.50+24.75p;
p=(1518.25-836.50)/24.75=681.75/24.75
Step-by-step explanation:
24.75 is about 25, so 681.75 is about 700, so that's about 28 people. If you don't have an option, do the math
Answer:
Equation: 24.75p+836.5=1158.25
Answer: p = 13
Step-by-step explanation:
Cost per player = 24.75
number of players = p
cost of bus = 836.50
total raised = 1158.25
Use the graph to find the slope (m) and y-intercept (b)
Answers
Answer:
Slope=4 y-intercept=(0,-21) or -21
Step-by-step explanation:
To find slope
m=-13-(-17)/2-1
m=4/1
m=4
To find y-intercept
y-(-17)=4(x-1)
y+17=4(x-1)
y+17=4x-4
Subtract both sides by 17
y=4x-21
y-intercept=-21
The sum of 3 times a number and half the same number and 4 is equivalent to 4 times the same number plus 1
Answers
Step-by-step explanation:
3n+1/2n+4=4n+1
3n+4n+1/2n=4+1
7n+1/2n=5
7.5n=5
Divide both sides by 7.5
5 divided by 7.5=
0.666
heelp me pls......
simplify each radical, then add or subtract. sqrt12 +sqrt27
Answers
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
simplify sqrt(12): [tex]\sqrt{12} = \sqrt{4 * 3} = \sqrt{4} * \sqrt{3} = 2 * \sqrt{3} = 2\sqrt{3}[/tex]
simplify sqrt(27): [tex]\sqrt{27} = \sqrt{9 * 3} = \sqrt{9} * \sqrt{3} = 3 * \sqrt{3} = 3\sqrt{3}[/tex]
substitute into original equation: [tex]\sqrt{12} + \sqrt{27} = 2\sqrt{3} + 3\sqrt{3}[/tex]
factor out sqrt(3): [tex]\sqrt{3} * (2 + 3)[/tex]
simplify: [tex]\sqrt{3} * 5 = 5\sqrt{3}[/tex]
(1,-4) (-3,-6)
midpoint and endponint
Answers
Answer:
Midpoint: (-1, -5)
Endpoint: (-3, -6)
Step-by-step explanation:
Midpoint:
(1-3)/2 and (-4-6)/2
(-1, -5)
A function f(x) = x^2 - 4 has a domain as the set of integers
of from 1 through 10, inclusive (including 1 and 10). For
how many values of x is f(x) positive?
Answers
Answer:
8
Step-by-step explanation:
f(x) = (x+2)(x-2)
Substituting x=1 into f(x):
f(1) = 3*-1
= -3
Since -2 & 2 touch the x-axis, 1 has a negative y value, 2 has a y value of 0, and all values from 2, are positive.
Hence,
3, 4, 5, 6, 7, 8, 9, 10 are all positive. Therefore, the answer is 8
This can be confirmed with a graph, as attached below.
Feel free to mark this as brainliest! :D
Jamal is using the distance formula to find the length, d, of the line segment. His work so far is shown. What is Jamal's next step?
Jamal should find the a(midpoint of each leg) b(midpoint of d) c(length of each leg)
by a(adding the x coordinate and y coordinate) b(squaring x coordinate and y coordinate) c(subtracting x coordinate and y coordinate)
.
Answers
Answer:
Jamal should find the Length of each leg by Subtracting the x coordinates and the y-coordinates and y-coordinates.
Step-by-step explanation:
Ansewer for Edmentum:)
Jamal's next step is : Jamal should find the length of each leg by subtracting x coordinate and y coordinate
What is right triangle?"It is a triangle whose one the angle measures 90°"
What is Pythagoras theorem?"In a right triangle [tex]c^{2} =a^{2} +b^{2}[/tex] where c is the hypotenuse and a, b are other two sides of right triangle."
What is the distance formula?"The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] "
For given question,
Jamal wants to find the length of 'd'
For right triangle in the figure, 'd' is the hypotenuse.
Jamal should find the other two sides of the triangle.
And then using Pythagoras theorem, Jamal can find the length of 'd'
So, Jamal need to find the length of each leg by subtracting x coordinate and y coordinate.
Therefore, Jamal's next step is : Jamal should find the length of each leg by subtracting x coordinate and y coordinate
Learn more about distance here:
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Plz help this is for a grade‼️ the ratio of males to females in the middle school is 6:8. If there are 126 make students,how many female students are there?
Answers
Answer:
168 girls
Step-by-step explanation:
126 boys and 168 girls.
Answer:
The answer should be 168 female students.
Step-by-step explanation:
Since the ratio of males to females is 6:8 and there's 126 male students, by dividing 126 by 6 you can get 21 then using that 21 you can multiply it by 8 to find how many female students there are which is 168 and dividing 126:168 by 21 you can get 6:8.
126 divided by 21=6
168 divided by 21=8
Help plz stuck on this question
Answers
Answer:
There are two questions please be specific
Stuck on this question! (Will mark as brainliest if correct)
Answers
Answer:
d. -8x+102
Step-by-step explanation:
I also checked my answer, BTW. You can too, but i KNOW that it's correct. :)
Point F is on line segment EG. Given EG = 20 and EF = 18, determine the
length FG.
Answers
Answer:
EF+FG =EG
18 + FG =20
FG = 20-18
FG = 2
Answer:
[tex]ef \: + \: fg \: = eg \\ \\ 18 + fg = 20 \\ \\ fg = 20 - 18 \\ \\ fg \: = \: 2[/tex]
help!!!!!!! i will pay, 15$ payment method of ur choice
Answers
round off 997 to the nearest 1000
Answers
Answer:
it would be 1000 because the last number is 7 which is greater than 5 so that rounds the 97 to the 100 and that would make to whole number altogether 1000!
Step-by-step explanation:
Hope this helps :)
Pls make brainliest :p
And have an amazing day <3
Math work, helpppppppppppppoooop
Answers
(BRAINLIEST)
There are 25 sanitizers in a box. A shop had a delivery of 35 such boxes. How many sanitizers were in this delivery?
Answers
Hope this helps !
Answer:
875
Exaplaination:
No. of sanitizer in a box= 25
No. of boxes deliver in a shop=35
Total sanitizer left?
25×35= 875
hope you get the answer
If John had 3 apples and Gave Jamal 2 how much left after you multiple by 6???
Answers
Answer:
6 apples
Step-by-step explanation:
Determine the focus of the parabola with the equation x2 - 6x + 5y = -34. Enclose answers in parentheses.
Answers
Answer:
jahahahaahhsydsywuwks
Gael deposited $600 in an account that earns 7% interest
compounded annually. If he makes no withdrawals or deposits, how
much interest will the account earn after 7 years?
Answers
Over 7 years, there would be 49% increase, so 600 (1.49) = 894
$894
Gordo is a fisherman. Darrin claims that Gordo over-estimates the size of his fish by 25%.
Gordo describes one fish as 40 cm long. What does Darrin claim is the length of Gordo’s
fish?
Answers
Answer:
The answer will be 30cm
Because 40 divided by 4 is 10 and times it by 3
an ordered pair has coordinates that have the same sigh. in which quadrants couls the point lie explain
Answers
Find the quotient. Your answer should be in simplest form.
-3/5 divided by (-3/4)
Answers
Answer:
-27/20
Step-by-step explanation:
i just went with the picture bc your question doesnt even match the picture, it shows adding not dividing. but change them to have common denominaators, then add the negative numbers, -12/20 + (-15/20), which is -27/20.
Answer:
4/5
sorry for bad writing
y+5.41=8.21 what is y
Answers
Answer:
2.80
Step-by-step explanation:
Answer= 2.8
Step-by-step explanation:
y+5.41=8.21
y= 8.21-5.41
y= 2.8
Rewrite the following equation in slope-intercept form. y - 10 = 4(x - 3)
Answers
Answer:
y=4x-2
Step-by-step explanation: