I need a, b, and c. I don’t quite understand this.
9514 1404 393
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.
__
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.
__
b) As we saw above, the vertex coordinates are (h, k) = (4, -4).
__
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.)
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
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]
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
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:
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!
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
HELp please!!!!!!!!!!!!!!!!!!!!!!11
Answer:
it’s 15x+30y-220
Step-by-step explanation:
Because you distribute and then you add the like terms
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
answer first and u will get a brain, a few free questions, thanks, or a rating.
Can someone please give me the 3 different combinations i dont know which combinations to do
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]
How many Wednesdays go into 180 days if you start on Monday?
How do you write equations for horizontal and vertical lines?
Answer:
y=_
x=_
Step-by-step explanation
horizontal for y=_
vertical for x=_
RATEE MEEE!?!!!!!!>???????????????????????!!!!!!!!!!!!!!!
Answer:
100/10 bbg ;)
Step-by-step explanation:
i forgot the name of the show but ykk
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 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)]
Find the change in temperature if the temperature rises -18⁰f to 15⁰f
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.
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
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
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 percentage of this grid is shaded?
b)
How many more squares need to be shaded
so that 80% of the grid is shaded?
Answer:
52% of the grid is shaded. You would need 7 more squares in order to get 80%.
Step-by-step explanation:
There are 25 boxes. You want to figure out how much each box is worth.
So,
You divide 100 by 25. You will get an answer of 4.
So now you know how much each box is worth.
There are 13 boxes shaded in, so you multiply 13 by 4 to get 52.
Keep adding boxes in order to get 80%. For example, 52%, 56%, 60%, until you get to 80%. Then see how many boxes you added up to get 80%.
We would need 7 more squares in order to get 80%. Thus, 52% of the grid is shaded.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
There are 25 boxes. we want to figure out how much each box is worth.
So,
100 / 25 = 4
Now, we know how much each box is worth.
There are 13 boxes shaded in,
so 13 x 4 = 52.
Keep adding boxes in order to get 80%.
For example, 52%, 56%, 60%.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
A trumpet cost $234.36 after tax. The price was $217 before tax. What was the percent of sales tax charged?
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:
write the ratio in simplest form 34 to 52
HELP PLS QUICK
Answer:
17 to 26
Step-by-step explanation:
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
Plz help I still have a 33% in my class and I’m trying to do as much imagine math as I can
Answer:
change in y 3-9/ change in x 4-1 =-6/3 = -2 there u go
Step-by-step explanation:
A rectangle has vertices (j,k) , (l,k) and (l,l). Find the fourth vertex
Answer:
(j,l)
Step-by-step explanation:
It's the only combination left
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