Drag each equation and coordinate to the correct location on the table. Not all equations or coordinates will be used. In the table below, quadratic equations are given in standard form. Rewrite each equation in the form that reveals the maximum or minimum value, and then identify the coordinate point of that extreme value.
Answers
Answer:
Standard Form Equivalent Form Extreme Values
y=x^2-6x+17 (x-3)^2+8 (3,8)
y=x^2+8x+21 (x+4)^2+5 (-4,5)
y=x^2-16x+60 (x-8)^2-4 (8,-4)
Step-by-step explanation:
1) Standard form:
y=x^2-6x+17
Equivalent Form:
Can be found using completing the square method.
[tex]y=x^2-6x+17\\y=x^2-2(x)(3)+(3)^2-(3)^2+17\\y=(x-3)^2-9+17\\y=(x-3)^2+8[/tex]
So, Equivalent form is: (x-3)^2+8
Extreme value:
Extreme values are basically the minimum and maximum value of the function.
Minimum Value will be found by finding derivative of the function:
The derivate is: 2x-6
Now, put the derivate equal to zero: 2x-6 = 0
[tex]2x=6\\x=6/3 \\x=3[/tex]
Maximum value can be found by putting minimum value in the given function:
Put x = 3 and solve:
[tex](3)^2-6(3)+17\\9-18+17\\9-1\\=8\\[/tex]
So, the extreme values is: (3,8)
2) Standard form:
y=x^2+8x+21
Equivalent Form:
Can be found using completing the square method.
[tex]y=x^2+8x+21\\y=x^2+2(x)(4)+(4)^2-(4)^2+21\\y=(x+4)^2-16+21\\y=(x+4)^2+5[/tex]
So, Equivalent form is: (x+4)^2+5
Extreme value:
Extreme values are basically the minimum and maximum value of the function.
Minimum Value will be found by finding derivative of the function:
The derivate of x^2+8x+21 is: 2x+8
Now, put the derivate equal to zero:
[tex]2x+8 = 0\\2x=-8\\x=-8/2 \\x=-4[/tex]
So, minimum value is: -4
Maximum value can be found by putting minimum value in the given function:
Put x = -4 and solve:
[tex]x^2+8x+21\\=(-4)^2+8(-4)+21\\=16-32+21\\=5[/tex]
So, Maximum value is: 5
So, the extreme values is: (-4,5)
3) Standard form:
y=x^2-16x+60
Equivalent Form:
Can be found using completing the square method.
[tex]y=x^2-16x+60\\y=x^2-2(x)(8)+(8)^2-(8)^2+60\\y=(x-8)^2-64+60\\y=(x-8)^2-4[/tex]
So, Equivalent form is: (x-8)^2-4
Extreme value:
Extreme values are basically the minimum and maximum value of the function.
Minimum Value will be found by finding derivative of the function:
The derivate of x^2-16x+60 is: 2x-16
Now, put the derivate equal to zero:
[tex]2x-16 = 0\\2x=16\\x=16/2 \\x=8[/tex]
So, minimum value is: 8
Maximum value can be found by putting minimum value in the given function:
Put x = 8 and solve:
[tex]x^2-16x+60\\=(8)^2-16(8)+60\\=64-128+60\\=-4[/tex]
So, Maximum value is: -4
So, the extreme values is: (8,-4)
Answer:
the dude above me i right i got i right on the test in edmentum
Step-by-step explanation:
Related Questions
- 5/6 * 1/8
Practice and problem solving
Answers
Answer:
- 6 and ?/6
Step-by-step explanation:
Just look at my pictute Haha. And btw it is negative because the fractions did not have the same sign as in one was positive and one was negative! Hope I helped! Please give me brainliest! Have a great day Adios. :)
On Saturday, Darnel earned $65 raking his neighbor's leaves and cleaning her garage. On Sunday, he earned $25 helping another neighbor rake leaves. He deposited his earnings in his bank account on Monday. What was the total change in Darnel's bank account relative to where it started?
Answers
Answer:
$90
Step-by-step explanation:
Calculation for the total change in Darnel's bank account relative to where it started
Based on the information given what will be the total change in Darnel's bank account relative to where it started will be the total amount he earned on both Saturday and Sunday
Total change=$65+$25
Total change=$90
Therefore the total change in Darnel's bank account relative to where it started will be $90
6 and 6x are like terms
true or false
Answers
Answer:
False
Step-by-step explanation:
Like terms have the same variable and are raised to the same exponent, and 6x has a variable of x while 6 has none at all, so they are not like terms.
Which is the volume of water in the fish tank shown rounded to the nearest
hundredth?
Answers
Answer:
4.69ft³
Step-by-step explanation:
1.5×2.5×1.25=4.69
Select the correct answer.
Which expression is equivalent to this polynomial expression?
(2x5 + 3y4)(-4x2 + 9y4)
Answers
Answer:
Is the A
Step-by-step explanation:
The correct option is option A i.e., [tex]-8x^{7} + 18y^{4}x^{5} - 4x^{2}y^{4} + 27y^{8}[/tex].
A polynomial expression [tex](2x^{5} + 3y^{4}) (-4x^{2} + 9y^{4})[/tex] is given.
We have to find out which option is equivalent to the given expression.
What do you mean by the polynomial expressions ?
A polynomial expression is the algebraic expression that consist of variables and coefficients.
As per the question ;
The given expression is ;
[tex](2x^{5} + 3y^{4}) (-4x^{2} + 9y^{4})[/tex]
Let's solve this expression.
i.e.,
= [tex](2x^{5} + 3y^{4}) (-4x^{2} + 9y^{4})[/tex]
= [tex]-8x^{7} + 18y^{4}x^{5} - 4x^{2}y^{4} + 27y^{8}[/tex]
So , the correct option is A.
Thus , the correct option is option A i.e., [tex]-8x^{7} + 18y^{4}x^{5} - 4x^{2}y^{4} + 27y^{8}[/tex].
To learn more about polynomial expressions click here ;
brainly.com/question/26685427
#SPJ2
Solve the system of linear equations by elimination.
-y-10 = 6
5x +y = -10
Answers
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(65,−16)
Equation Form:
x=65,y=−16
Step-by-step explanation:
Hey there!
The solution to the given system is (0, -10)
To solve using elimination, we have to add the equations together, and the "y"s will cancel out, and then solve the equations:
5x - 10 = 6x - 10
Now solve.
Add "10" to both sides:
5x = 6x
Subtract "5x" from both sides
0 = x
Now, we plug in the solved "x" value in an equation to solve for "y".
5(0) + y = -10
y = -10
We now know that the solution to the given system is (0, -10)
Hope this helps! Have an amazing day, and remember, you've got this!!
please help
g(x) = -x - 1
Answers
Answer:
g(x) = -1
Hope this helps.
Step-by-step explanation:
Describe the strength and sign of the relationship you expect for each pair of variables. Explain your reasoning.
Used car price and original sale price of the car.
Used car price and number of cup holders in the car.
Used car price and number of oil changes the car has had.
Used car price and number of miles the car has been driven.
Answers
Answer:
i dont get it
Step-by-step explanation:
The length of the rectangle is increased by 10%.
The width of the rectangle is increased by 5%.
Find the percentage increase in the perimeter of the rectangle.
(please look at the photo)
Answers
Answer:
8% increase
Step-by-step explanation:
The length after the increase:
30 x 1.1 = 33cm
The width after the increase:
20 x 1.05 = 21cm
New perimeter:
2(33 + 21) = 108 cm^2
Old perimeter:
2(30 + 20) = 100 cm^2
Percentage increase of area:
108 / 100 = 1.08 = 8% increase
Answer:
length_20 cm breadth_30 cm
Step-by-step explanation:
width of the rectangular_ 5/:. length of rectangular_10/:. primeter of rectangular_? now perimeter of rectangular_2(l+b). 2(20+30) __100#
The perimeter of a triangle is 24 ft. The second side is two feet longer than the first. The third side is two feet longer than the second. What are the lengths of the sides?
Answers
Answer:
6; 8; 10
Step-by-step explanation:
First side: x
Second side: x+2
Third side: x+4
x + x + 2 + x + 4 = 24
3x + 6 = 24
3x = 18
x=6
First side: 6
Second side: 8
Third side: 10
Could you guys help me with this I’m stressed out ill give brainliest please don’t answer if you don’t know thank you
Answers
Answer:
$146.66
Step-by-step explanation:
I bopped this into a percentage calculator and this is what I got
Need help asapppppppp
Answers
Answer:
It is not a function.
Step-by-step explanation:
Input (x)
Output (y)
An input can never have two outputs
2 = 20
2 = 40
makes it not a function
10,10,10,20 i hope that helps but if not its cause i dont really understand the question
Write the equation of the line in slope intercept form that has a slope of -4 and a
y-intercept of -8.
Answers
Answer:
y=-4x+-8
Step-by-step explanation:
Put me the brainliest please
Melissa buys 2.5 pounds of salmon and 1.25 pounds of swordfish. She pays a total of $31.25, and the swordfish costs $ 0.20 per pound less than the salmon. What would be the combined cost of 1 pound of salmon and 1 pound of swordfish?
Answers
Please answer if so you get brainliest
Answers
open notes and think about it
A doctor collected data on how many hours children of different ages slept in a day. Data for 5 participants are
shown below.
Answers
The answers is the picture I posted. I did in khan academy and it was right.
The data values of the scatter plot are (x,y) = (1,13), (2,11), (3, 10), (5,9) and (8,8)
How to represent the table on a scatter plot?The table of values is given as:
x: 1 2 3 5 8
y: 13 11 10 9 8
This means that the data values are:
(x,y) = (1,13), (2,11), (3, 10), (5,9) and (8,8)
See attachment for the scatter plot
Read more about scatter plots at:
https://brainly.com/question/6592115
Can someone help me with this to?
Answers
Part b I’m not sure about. One person would have to but 4 video games I guess
how do you do this , i need help!!
Answers
Answer:
i dont know
Step-by-step explanation:
Answer:
112º
Step-by-step explanation:
(you may need a calculator for this)
first let's start with what we know, we know a triangle has 180º. We also know a line has 180º. if you know the line has 180º, then ? + 126 º = 180º. so if you subtract 126 from 180, you get 54. now lets look at the triangle, we know the triangle has 180º in total. we already know one angle is 58º, and we just figured out the other is 54º. if you do 54+58, you get 112. remember, the triangle has 180 degrees in total, and two of them equal 112º, so 180 - 112 is 68. almost there! now we have to do the line trick again, because on the line, 68 + x = 180. 180- 68 is 112, so the answer is 112º. Hope this helps :D
Which expression shows the prime factorization of 66? please i need help so bad its a test
Answers
Answer:
B
2 times 3 times 11
Step-by-step explanation:
Help I don’t get it
Math
Answers
Answer:
Thats right
Step-by-step explanation:
You typed the right answer :/
If the parent function is fx) = x^3 which transformed function is shown in the graph?
A. g(x) = (x-3)2
B. g(x) = (x+3)^3
C. g(x) = x^3 + 3
D. g(X) = x^3-3
Answers
Answer:
g(x) = (x-3)³ is the transformed function.
Step-by-step explanation:
Horizontal shift:
If f(x) is the parent function.
Then horizontal shift can be expressed as:
, will shift left units.
[tex]y = f(x - c)[/tex], will shift [tex]f(x)[/tex] right c units.
Given the parent function
f(x) = x³
From the graph, it is clear that the transformed function is indicating that the parent function has been horizontally shifted right 3 units.
Therefore, according to the rule, [tex]y = f(x - c)[/tex]:
g(x) = (x-3)³ is the transformed function.
From the graph,
The Red graph indicates the parent function i.e. f(x) = x³ The Blue graph indicates the transformed function i.e. g(x) = (x-3)³It is clear that the blue graph is obtained when the parent function has been horizontally shifted right 3 units.
Therefore, g(x) = (x-3)³ is the transformed function.
please help me please will give brainliest to anyone
Answers
Answer:
[tex]x^4+x^2-12[/tex]
Step-by-step explanation:
We'll write the polynomial using only the roots required to simplify calculations. However, it states the final answer should not have a radical or complex number in. Therefore, we need to rid them:
[tex](x+\sqrt{3})(x-\sqrt{3})(x-2i)(x+2i)[/tex]
Expanding this, we get:
[tex](x^2-3)(x^2+4),\\\fbox{$x^4+x^2-12$}[/tex].
i need help with geometry
Answers
Answer:
B. rectangle, square, quadrilateral, parallelogram, rhombus
Step-by-step explanation:
A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles. A trapezoid is a quadrilateral with exactly one pair of parallel sides.
An object dropped from a height of h feet will take t seconds to fall all the way to the ground, according to the
following equation.
16t2 - h = 0
The Eiffel Tower in Paris, France is 900 feet tall.
How many seconds will it take an object dropped from that height to fall all the way to the ground?
Answers
Answer:
7.5 seconds.
Step-by-step explanation:
16t^2 - h = 0
16t^2 - 900 = 0
t^2 = 900/16
t = √900/√16
= 30/4
= 7.5 seconds.
6 pounds of candy cost $22.44 how much does it cost of 10 pounds
Answers
$37.40
This is because
22.44/6= 3.74
and 3.74*10= 37.4
So answer is:
$37.40
Answer:
10 pound=$37.4
Step-by-step explanation:
$22.44 divide by 6 = one pound $3.74
$3.74*10= $37.4
4. The money in Mrs. Finch’s savings account is earning 1.45% interest. Which number below is greater than 1.45%
A) 0.009
B) 0.019
C) 0.0032
D) 0.0117
Answers
0.019 = 1.9%
What is the value of y?
Answers
Answer:
[tex] {y} = 6\sqrt{3} \:units [/tex]
Step-by-step explanation:
By Pythagoras Theorem:
[tex] {y}^{2} = {(9 + 3)}^{2} - {(6)}^{2} \\ \\ {y}^{2} = {(12)}^{2} - {(6)}^{2} \\ \\ {y}^{2} = 144 - 36 \\ \\ {y}^{2} = 108 \\ \\ {y} = \sqrt{108} \\ \\ {y} = \sqrt{36 \times 3} \\ \\ {y} = \sqrt{ {6}^{2} \times 3} \\ \\ {y} = 6\sqrt{3}\:units [/tex]
#Homework Help Please
Answers
Answer:
can you take a picture of the options?
Step-by-step explanation:
Solve the following system of equations:
y=2x + 1
y = -x+4
x= ?
y=?
Answers
Answer:
x= 1, y=3
Step-by-step explanation:
y= 2x +1
y= -x +4
Those two equation are in a system that means they need to be true in the same time. Just like I would say look for a car that is red and is a truck in this case we look for x and y is true that y = 2x+1 and is true that y= =x+4.
so y= 2x+1 but y is -x+4 so substitute
-x+4 = 2x +1, add x on both sides
4= 2x+x +1, subtract 1 from both sides
4-1 = 2x +x, combine like terms
3 = 3x , divide both sides by 3
x=1
if x=1 we substitute in y= -1 +4 = 3
The distance around a closed shape can be expressed as 3 times the length of side s or 3s draw an example of this geometric shape (what shape do I draw)