Suppose a parabola has an axis of symmetry at x=-1 a maximum height of 6 and passes through point -2,1. Write the equation of the parabola in vertex form
Answers
[tex]y = a(x-h)^{2}+k[/tex]
There is some info in the question that can be used to our advantage. The best way to understand the axis of symmetry thing is to know that this is where the parabola meets its highest or lowest value (depending on the sign of 'a' in the beginning of the above equation). It meets its highest or lowest points whenever (x-h) = 0. This means the value at this point is only equal to whatever k is. If 'a' is positive this is a minimum, because (x-h)^2 is always positive and if a is positive then the function increases on either side of the axis of symmetry. If 'a' is negative you get the opposite effect.
Anyway, if we need (x-h) and we look at the point x = -1, then we need h to also be equal to negative one so that it is 0. (-1 - (-1)) = 0. This gives us our symmetry condition, and we also know that the max height is 6. That means when (x-h) = 0 the value of the function is k from the above equation, hence k = 6. Now we have everything except for the value of 'a'. The first thing we can tell is that it is negative. That is because the parabola has a maximum value. The coefficient 'a' determines whether there is a maximum or minimum.
Now, we have to figure out how to get 'a' such that it goes through the point (-2,1). To do that we can take our equation with the values of h and k that we have already figured out and solve for 'a' when x = -2 and y = 1:
[tex]y = a(x-(-1))^{2}+6 = a(x+1)^{2}+6[/tex]
Now we plug in the (x,y) values of interest:
[tex]1= a(-2+1))^{2}+6 = a+6 \iff a = -5[/tex]
then our final equation for the parabola is:
[tex]y = -5(x+1)^{2}+6[/tex]
You can also plot this on desmos.com to see it for yourself.
Related Questions
4. which property is illustrated by the following statement?
2x(6)=(6)2x
A. associative property of addition
B. communtative property of multiplication
C. inverse property of multiplication
D. communtative property of addition
5. which property is illustrated by the following statement?
5g+7=7+5g
A. communtative property of multiplication
B. Inverse property of multiplication
C. communtative property of addition
D. associative property of addition
Answers
A B = B A
Answer:
B ) Commutative property of multiplication
Another statement:
5 g + 7 = 7 + 5 g
A + B = B + A
Answer:
C ) Commutative property of addition.
The answer for #5 is C.
Line QR bisects angle PQS. Solve for x and find measure PQS:
m
Answers
Line QR bisects angle
PQS. Solve for x and find measure PQS:
m<PQS = 4x - 6, m<PQR = x + 11 ...?
m<PQR = (1/2) (m<PQS) = (1/2)( 4x - 6)
so x + 11 = 2x - 3 implies x =14
and then m<PQS = 4x - 6 =50°
Please explain this problem.
Answers
-----|--------
35 | 40
-----|--------
42 | 47
-----|--------
49 | 54
-----|--------
The "In" numbers are +2 while the "Out" is +5.
I hope this helps! :D
The decimal number 0.66 is an example of a repeating decimal.
True
or
False
pls answer quick
Answers
Answer:
the anwser is FALSE
Step-by-step explanation:
The total cost in dollars to produce q units of a product is C(q). Fixed costs are $13000 . The marginal cost is C'(q)=0.006q^2-q+50.
Estimate C(170) , the total cost to produce 170 units.Find the value of C'(170). Then combine these to find C(171).
Answers
C(170) = 0.002(170)^3 - 1/2(170)^2 + 50(170) + 13000 = 9826 - 14450 + 8500 + 13000 = $16,876
C'(170) = 0.006(170)^2 - 170 + 50 = 173.4 - 120 = $53.40
Therefore, C(171) = C(170) + C'(170) = $16,876 + $53.40 = $16929.40
To find the cost of production for 170 units, consider both fixed costs and variable costs (the integral of the marginal cost function). The cost of producing 171 units can be estimated by adding the marginal cost for the additional unit.
Explanation:The quantity of interest is C(170), the total cost to produce 170 units. To estimate this value, you can calculate the fixed costs plus the integral of the marginal cost from 1 to 170 (the number of items produced).
So, first, calculate the fixed costs which is given as $13000.
Next, estimate the total variable costs, which is the integral of the marginal cost function over the range from 1 to 170 units. Given marginal cost function is C'(q) = 0.006q^2-q+50. Use the power rule to integrate the function, then evaluate it at q=1 and q=170 and subtract.
The value of C'(170) is simply the value of the marginal cost function at q=170.
After finding the value of C(170) and C'(170), the total cost to produce 171 units, C(171), is approximately the total cost to produce 170 units plus the marginal cost to produce the 171st unit.
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For the fruit punch, keira needed 2 gallons of grape juice. she already had 2 quarts of grape juice. grape juice comes in bottles of 1 pint. how many bottles of grape juice does she need to buy? bottles
Answers
so she needed 8 qts.....she had 2....so she still needs 6 qts.
1 qt = 2 pints...so 6 qts = (6 x 2) = 12 pints...and each bottle is 1 pints...so she needs 12 bottles
# of Songs:Cost
6:$7.20
7:$8.40
8:$9.60
Cedric buys songs at a store that charges $1.20 per song. Shumeka buys songs at a different store. The table shown here gives the cost when she buys 6, 7, and 8 songs.
Are songs more expensive at Cedric’s store or Shumeka’s store?
A) Cannot be determined
B) Cedric's store is more expensive.
C) Shumeka's store is more expensive.
D) Songs cost the same at both stores.
Answers
Answer:
Songs cost the same at both stores.
Step-by-step explanation:
The formula c=5/9(f-32) is used to convert the temperature in degrees fahrenheit (
f. to the temperature in degrees celsius (
c. what is the temperature in degrees celsius (
c. that is equal to 113 degrees fahrenheit (
f.?
Answers
c = 5/9(f - 32)
c = 5/9(113 - 32)
c = 5/9(81)
c = 405/9
c = 45 <===
The conversion of fahrenheit to degree celsius for f = 113 is 45 degree celsius
What is a mathematical expression?
When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.
Given, formula of temperature conversion of degree celsius to fahrenheit
c=5/9(f-32)
If f = 113
then putting the value on the equation, we get
c = 5/9(113-32)
c = 5/9(81)
c = 5*9
c = 45 degree celsius
Therefore, The conversion of fahrenheit to degree celsius for f = 113 is 45 degree celsius
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What is the value of the discriminant in the equation shown below?
x^2+3x-6=0
...?
Answers
Discriminant = b^2 - 4ac
a = 1
b = 3
c = -6
3^2 - 4(1x-6)
9 - (4 x -6 )
9 - -24 = 33
Therefore it has 2 real roots
3^2 - 4(1)(-6)
[a] x^2 [+b] x [+c] = 0[1] x^2 [+3] x [-6] = 09 - 4(1)(-6) = 9 - (-24)
=33
Solve (x 6)(x - 4) = -16
Answers
2x= -14
x= -7
Answer:
{-4, 2} Original poster forgot to add the + sign
Step-by-step explanation:
Solve (x + 6)(x - 4) = -16
{-4, 6}
{-4, 2}
{-12, 22}
Odyssey
Substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place. Use the approximation 3.14 for pi. C=44. C stands for circumference.
Answers
then
c=2pi r or d*pi44=d pi44/pi=d
then d= 44/3.14
r= 22/3.14
divide 56 in a ratio of 5:3
Answers
5 x 7 is 35
3 x 7 is 21
___________
So the answer is 35:21 .
20 is 50% of what number? If necessary, round to the nearest tenth.
Is it 10.0?
Answers
20+20=40
40 is the correct answer.
20 is 50 percent of the number 40.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let 20 is 50% of the number x.
Now, 50% of x=20
0.50×x=20
0.5x=20
x=20/0.5
x=40
Therefore, 20 is 50 percent of the number 40.
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Mrs. Curtis wants to buy online tickets for a concert. Two options are given here.
Option 1: $53 for each ticket plus a shipping fee of $10
Option 2: $55 for each ticket and free shipping
What is a system of equations to represent the costs of the tickets?
Express your equations in the form of y=mx+by=mx+b where x is the number of tickets purchased and y is the total cost.
Option 1:______________
Option 2: ______________
Answers
Option 2: y=55x
(1.8 * 10^2) * (5 * 10^2)
Answers
If the sum of the measures of the interior angles of a convex polygon is 2160o, how many sides does the polygon have?
Answers
180n = 2160 + 360
n = 2520/180
n = 14
so, the polygon have 14 sides.
hope this help
What is 117.28 rounded to the nearest 10 cents?
Answers
Katie is selling lemonade for 1.50 pee cup. she decides to put them on sale for 0.90. what percent discount did she give her on the lemonade
Answers
1 - .6 = .4 (40%) //must reverse because 60% is the current selling price not discount
please help me with this problem thanks!
Answers
Answer= 110400 sq. mi
Renna pushed the button for the elevator to go up, but it would not move. The weight limit for the elevator is 450 kilograms, but the current group of passengers weighs a total of 750 kilograms. Renna wants to determine how many 70-kilogram passengers need to get off the elevator.
Let p represent the number of excess passengers. Write an inequality to determine the number of passengers who need to get off the elevator to meet the weight requirement.
Answers
Passengers weight: 750 kg
Excess weight: 300 kg
Number of 70 kg - passengers: p
Inequality:
70p ≥ 300 kg
Solution of the inequality:
p ≥ 300/70
p ≥ 4.3
Given that p is integer, p ≥ 5
Of course, p must also be less than the initial number of passengers.
Factor completely: 21x3 + 35x2 + 9x + 15 ...?
Answers
= 7 x² ( 3 x + 5 ) + 3 ( 3 x + 5 ) =
= ( 3 x + 5 ) ( 7 x² + 3 )
That`s all. Thank you.
Answer:
The complete factored form of given polynomial [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]
Step-by-step explanation:
Given polynomial [tex]21x^3+35x^2+9x+15[/tex]
We have to factorize the given polynomial completely.
Consider the given polynomial [tex]21x^3+35x^2+9x+15[/tex]
We will solve it by grouping of terms,
Grouping is collecting terms having some factors common
Taking [tex]7x^2[/tex] common from first two term and 3 from last two terms , we have,
[tex]21x^3+35x^2+9x+15[/tex]
[tex]\Rightarrow 7x^2(3x+5)+3(3x+5)[/tex]
Now taking (3x +5) common from both terms , we have,
[tex]\Rightarrow (7x^2+3)(3x+5)[/tex]
Thus, the complete factored form of given polynomial [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]
Which of the following would you round and estimate to a sum of 11?
3.41 + 8.051
3.65 + 7.992
4.25 + 8.103
4.89 + 7.431
Answers
Answer:
3.41+8.051
Step-by-step explanation:
A box of rice is 19 centimeters long, 12 centimeters wide, and 3.5 centimeters deep. The volume of the box is the product of its length, width, and height. What is the volume of the box?
Answers
the price of a car increases in the ratio 11:8. What is the new price of a car which originally cost 25600?
Answers
25,600/11= 2,327
2327*8= 18,618
hope this helped
the product of two integers is -21. the diference between the two integers is -10. the sum of the two integers is 4. what are the two integers
Answers
7 x -3 = -21
difference = -10
the sum = 4
hope this helps you
If martha earns $3.25 per hour for baby-sitting, how much will she earn in: 2.5 hours? 4.0 hours? 5.5 hours?
Answers
In 4.0 hours: $3.25 * (4) = $13.00
In 5.5 hours: $3.25 * (5.5) = $ 17.875 → Round to: $17.88 .
____________________________________________
Answer: Martha will earns for 2.5 hours of baby sitting [tex]\approx\$8.13[/tex]
She will earns for 4.0 hours of baby sitting =[tex]\$13[/tex]
She will earns for 5.5 hours of baby sitting =[tex]\approx\$17.88[/tex]
Step-by-step explanation:
Given: Martha earns for each hour of baby sitting = $3.25
Then, Martha will earns for 2.5 hours of baby sitting =[tex]2.5\times3.25=\$8.125\approx\$8.13[/tex]
She will earns for 4.0 hours of baby sitting =[tex]4.0\times3.25=\$13[/tex]
She will earns for 5.5 hours of baby sitting =[tex]5.5\times3.25=\$17.875\approx\$17.88[/tex]
What is the leg length of an isosceles right triangle with a hypotenuse of 32 inches?
Answers
that means that those are the legs
a^2+b^2=c^2
a and b are legs and c is the hypotonuse
a=b
2a^2=c^2
c=32
2a^2=32^2
2a^2=1024
divide both sides by 2
a^2=512
sqrt both sides
a=16√2
the legnth of each leg is 16√2 or aprox 22.63 inches
this year 90 students signed up for the group Talent contest if all the groups have the same number of students how many groups could be formed
a. 4 or 5 groups
b. 5 or 6 groups.
c. 4 or 6 groups
d. 4 or 9 groups
Answers
help :(
Which situations can be represented by a linear function?
Select each correct answer.
a. Every year, Luisa puts $10 into her savings account.
b. Every day, the number of bacteria in the dish is 3 times what it was the previous day.
c. A country's population increases by 0.8% each year.
d. The barrel leaks 0.5 L of water each day.
Answers
The barrel leaks 0.5 L of water each day.
Every year, Luisa puts $10 into her savings account.
Give the excluded value(s) for the following fraction.
y+5/y^2+4y-32
Answers
The exluded values are lying in the y and we hav eto find them :[tex]y^2+4y-32=(y+8)*(y-4)=0[/tex]
According to the info above,[tex]y+8=0 or y-4=0[/tex]
y is -8 and 4.
That's all!
Answer:
y is -8 and 4.
Step-by-step explanation: