I need a, b, and c. I don’t quite understand this.
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Answer:
a) y = (x -4)² -4
b) (4, -4)
c) translated 4 right, 4 down
Step-by-step explanation:
a) Apparently "graphing form" is a reference to "vertex form." That form is ...
y = a(x -h)² +k . . . . . . parabola with vertex (h, k) and vertical scale factor 'a'
The coefficient of x² in your given equation is 1, so a=1. The values of h and k can be found as follows.
'h' is the opposite of half the x-coefficient in your equation, so is h = -(-8/2) = 4. The value of k is the square of h, subtracted from the constant in your equation: k = 12 -h² = 12 -16 = -4. (This applies when a=1, as here.) These calculations are the "cut to the chase" version of "completing the square."
The method of "completing the square" has you consider the x-terms separately from the constant term:
y = (x² -8x) +12
To "complete the square", you want to make the terms in parentheses be a perfect square trinomial. You do that by adding the square of half the x-coefficient. In order to keep the same equation, you need to subtract an equivalent amount outside parentheses:
y = (x² -8x +(-8/2)²) +12 -(-8/2)² . . . . . add and subtract (-8/2)²
y = (x -4)² +(12 -16)
Then the vertex form is ...
y = (x -4)² -4 . . . . and the vertex is (h, k) = (4, -4).
The graphing calculator plot attached confirms this vertex value.
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The problem statement tells you that you can also find this form by averaging the x-intercepts. If you factor your equation, you get ...
y = (x -6)(x -2)
The x-values that make these factors zero {6, 2} are the x-intercepts. Their average (6+2)/2 = 4 is the x-coordinate of the vertex (h). You can find the y-coordinate of the vertex by evaluating y when x=4: y = 4² -8·4 +12 = -4. So, the vertex by this method is (h, k) = (4, -4), and the equation in graphing form is ...
y = (x -4)² -4 . . . . as above.
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b) As we saw above, the vertex coordinates are (h, k) = (4, -4).
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c) The vertical scale factor 'a' is 1, so the only transformation done on the graph is to move the parent vertex (0, 0) to the location (4, -4). That is, the graph has been translated 4 units right and 4 units down. (In the attached, the parent function is shown with a dashed line.)
on a certain day the temperature at midday was 14°c.By midnight the temperature had fallen by 17°c what was the temperature at midnight
Answer:
-3c
Step-by-step explanation:
Answer:
-3c
Step-by-step explanation:
according to my calculations this is right
Graph the inequality on the axes below.
(Can someone please help)
Answer:
Step-by-step explanation:
first put the inequality into slope intercept form (y-mx+b)
x-3y</=18
-3y</=-x+18
y>/=1/3x-6 (you have to flip the sign since you are dividing by a negative number)
then graph it (i attached a picture)
to figure out what side to shade in you can substitute the point (0,0) in for x and y. if it is true you shade in the part of the graph that includes (0,0).
0>/=1/3(0)-6
0>/=-6
solve for x it is a parallelogram
pls help
Answer:
x = 5
Step-by-step explanation:I hope that this answer will help youAnswer:
[tex]3x + 2 = 17 \\ 3x = 15 \\ \boxed{x = 5}[/tex]
5 is the right answer.Write the equation of the line that passes through points (-4, 5) and (0,13) in slope-intercept form.
Answer:
The answer is
[tex]y = 2x + 13[/tex]
Step-by-step explanation:
Remember:
[tex]Slope-intercept form: \: \\ y = mx + b \\ \\ m = slope \\ b = y - intercept[/tex]
[tex]M = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
First: Find the slope.
[tex]M = \frac{13 - 5}{0 - ( - 4)} = \frac{8}{4} = 2[/tex]
.
Second: Solve for the y-intercept
[tex]y = mx + b \\ 5 = 2( - 4) + b \\ 5 = - 8 + b \\ \frac{+ 8 = + 8 \: \: \: \: \: \: \: \: }{13 = b} [/tex]
.
Third: Plug in.
[tex]y = mx + b \\ y = 2x + 13[/tex]
I need the equation that passes through this point( and yes its a dif one)
Answer:
Step-by-step explanation:
this is okay ... use the point-slope formula [y-y1=m(x-x1)] with your given point.. also m is the slope.. which as is.. is undefined.. so just leave it like that.. the teacher is making this too abstract thou.. to make sense
y-2=m(x-(-3))
y-2 = m(x+3)
y-2 = mx +3m
y = mx +3m +2
that's all you could do for now.. until the slope is defined :)
Answer:
y-2=m(x-(-3))
y-2 = m(x+3)
y-2 = mx +3m
y = mx +3m +2
Step-by-step explanation:
Choose the graph of this equation. y = 2.5x
BRAINLIST IF RIGHT!!!!
Answer:
The First Graph (top left)
Step-by-step explanation:
bottom left: y = 3x
top right: y = 2x
bottom right: y = 3x
The top left is the only correct one
HELp please!!!!!!!!!!!!!!!!!!!!!!11
Answer:
it’s 15x+30y-220
Step-by-step explanation:
Because you distribute and then you add the like terms
A seed company planted a floral mosaic of a national flag. The perimeter of the flag is Determine the flag's width and length if the length is ft greater than the width.
Answer:
Step-by-step explanation:
lag is Determine the flag's wlag is Determine the flag's wlag is Determine the flag's w this mena that the wiatgh
Answer:
I need help on this.
Step-by-step explanation:
A trumpet cost $234.36 after tax. The price was $217 before tax. What was the percent of sales tax charged?
Here are four numbers.
0.43 3/7 43.8% 7/16
Write these numbers in order of size.
start with the smallest number.
First convert all th fractions into decimal :
3/7 =0.428
7/16=0.4375
0.43=remain same (already given in decimal form)
43.8%=0.438
now arrange them in one row (horizontally) then it will be easy to arrange it.
0.428 , 0.4375 , 0.43 ,0.438
=0.428 , 0.43, 0.4375 ,0.438
= ans) 3/7, 0.43, 7/16, 43.8%
If 7 workers take 500 hours to finish a project, how long will it take 14 workers to complete the same project?
Answer:
250 hours
Step-by-step explanation: increasing the number of workers will make the project go faster. So they multiplied the 7 by 2 so now there are 14 workers so then the time it'll take to finish the project would be cut in half because now they have twice the numbers of workers. correct me if I'm wrong
The triangle below is a right triangle Find the length of the missing side provide in simplified radical form
Answer:
[tex]2\sqrt{10}[/tex]
Step-by-step explanation:
Take [tex]a^{2} +b^{2} +c^{2}[/tex], let x represent a, 9 represent b, and 11 represent c.
Now, plug your variables into the equation:
[tex]x^{2} +9^{2} =11^{2}[/tex]
Simplify:
[tex]x^{2} +81=121[/tex]
Subtract:
[tex]x^{2} =40[/tex]
Take the square root of 40:
[tex]x=2\sqrt{10}[/tex]
Help pls 6th grade math i will give brainliest
Answer:
It is c
Step-by-step explanation:
(y x 40) + (y x 8)
40y + 8y
48y
y x 48 = 48y
Please help! This is due soon!
Answer:
try looking at the codes in it, in the coding it says the answer!
Step-by-step explanation:
my brother told me, I tryed it out and it worked, just don't get caught!
I thought of a 2-digit number. It's a multiple of 9 and the sum of its digits is five times smaller than the number itself. What is my number?
Step-by-step explanation:
Since the sum of the digits must be an integer, the number itself must also be a multiple of 5.
Lowest common multiple of 5 and 9 = 45.
Therefore the number could be 45 or 90.
5(9 + 0) =/= 90, so 90 is incorrect.
Since 5(4 + 5) = 45, 45 is the answer.
Answer: 45
Step-by-step explanation:
We know that it has to be a 2-digit number. Its the multiple of 9. We see there is a number in the question. Five. I simply took 9 and multiplied it by 5 which gave me a total of 45.
For the school play, the advance tickets cost 3, while tickets at the door cost 5. Thirty more tickets were sold at door than in advance, and was collected. How many of each kind of ticket were sold? Write your answer in a sentence.
Answer:
Number of tickets sold in advance = 310
Number of tickets sold at the door = 340
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
For the school play, the advance tickets cost $3, while tickets at the door cost $5. Thirty more tickets were sold at the door than in advance, and $2630 was collected. How many of each kind of ticket were sold?
The explation of the answer is now given as follows:
Let a represents number of tickets sold in advance. Therefore, we have:
a = number of tickets sold in advance at $3 each
a + 30 = number of tickets sold at the door at $5 each
The total amount collected can be represented by this equation:
3a + 5(a + 30) = 2630
Solving for a, wee have:
3a + 5a + 150 = 2630
8a = 2630 - 150
8a = 2,480
a = 2,480 / 8
a = 310
Therefore, this implies:
Number of tickets sold in advance = 310
Number of tickets sold at the door = a + 30 = 310 + 30 = 340
What is the y-intercept of the function f(x) = -2/9x + 1/3
Answer:
Step-by-step explanation: substitute 0 in for x for the y intercept
LAST ONE I-I-I PROMISE >
Answer:
Step-by-step explanation:
Putting value of z = 3
6(3)2+ 2(3) + 10
6(9) + 6 + 10
54 + 16
70
answer first and u will get a brain, a few free questions, thanks, or a rating.
How many Wednesdays go into 180 days if you start on Monday?
I don't understand how to do this
9514 1404 393
Answer:
B, E
Step-by-step explanation:
You are give a table of values of x and f(x). You are told that g(x) = (1/2)f(x), and you are asked for points (x, g(x)) that match that description.
It can be useful to mentally, or actually, add a third column to the table that shows the values of g(x). Each of those is half the corresponding value of f(x), because that is what g(x) = (1/2)f(x) means.
Having done that, you can then compare the ordered pairs (x, g(x)) to those in the answer list to see which ones match. The ones that match are highlighted in green in the attachment:
(-1, -2) . . . . . . 2nd choice
(6, 3/2) . . . . . 5th choice
A salesman needed to sell a used car. He priced it at $4,500 the first day it was on the
market. The second day he reduced the price by 12%. What was the price of the used car after this reduction?
Answer:
$3960
Step-by-step explanation:
12% of $4,500 is 540.
Subtracting the 12% means taking away $540 from $4,500, which gives you $3960
1. Y+7=-10
2. 8=x+5
5. r+4=7
6.-11+y= -8
Answer:
1. 3
2. 3
5. 3
6. 3
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. y = -17
2. x = 3
5. r = 3
6 y = 3
What is the completely factored form of 2x^2-32?
Step-by-step explanation: 2(x+4)(x-4) is the factored form of 2x^2-32.
Answer:
2[(x+4)(x-4)]
Step-by-step explanation:
2x2-32
2(x2-16)
2(x2-4^2)
2[(x+4)(x-4)]
The corresponding sides of triangles ABC and DEF are congruent. Which statements are always true for triangles ABC and DEF ? Select all that apply.
Which situation is best represented using a negative integer?
a deposit of $35 into a bank account
the temperature decreasing by 18º
an additional 5 gallons of gas being put into a car
a student reading today for 20 minutes longer than yesterday
Answer:
B. the temperature decreasing by 18º
Step-by-step explanation:
decreasing means to take away or less so therefore its b
Answer:
B. the temperature decreasing by 18º
Step-by-step explanation:
i just took it
What is the slope of the line with equationy-3=-x-2)?
3)
(42).
Answer:
Step-by-step explanation:
-3 = -x - 2
the equation is a bit hard to read in your questions but if that is the correct equation then the slope is -1
Can someone please give me the 3 different combinations i dont know which combinations to do
Which expression shows a way to find 438 + 197 + 362?
Answer:
.
Step-by-step explanation:
we are asked to write an expression that shows how to multiply 4 and 362 using place value ans expanded form. The expanded form of 362 is 300 + 60+ 2. IN this case, the expression is 4*(300 +60+ 2) that is we distribute 4 to the numbers inside that is 1200 + 240 + 8 equal to 1448