1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alisha [4.7K]
3 years ago
13

Find the vertex, focus, and directrix. y = 1/24(x+1)² - 3. 

Mathematics
2 answers:
Vedmedyk [2.9K]3 years ago
6 0
y = \frac{1}{24}(x+1)^2 - 3\\\\y+3 =\frac{1}{24}(x+1)^2\ \ / *24\\\\ (x+1)^2 = 24(y+3)

This   is  an  equation  of  a  parabola  that  opens  upwards.

Its \ standard \ form: \\(x-h)^2=4p(y-k)\\ (h,k)=(x,y) \ coordinates \ of \ the \ vertex\\\ (h,k)=(-1,-3) \\\\axis \ of \ symmetry: \ x= -1\\ \\4p=24\ \ /:4\\p=6

focus:(h,k+p)=(-1,-3+6)=(-1,3) \\ \\directrix: \ y=k-p=-3-6=-9


liq [111]3 years ago
5 0

the\ equation\  in\  the\ form\ (x-h)^2=4p(y-k)\ is \ a\ parabola\\with\ a\ vertex\ at\ \  (h,\ k), \\a\ focus\ at\ \ (h,k+p)\\\ and\ a\ directrix\ \ y = k - p \\\\ y = 1/24(x+1)^2 - 3\ \ \ \ \Rightarrow\ \ \ y+3 = 1/24(x+1)^2\ /\cdot24\\\\ 24\cdot(y+3)=(x+1)^2\\\\(x+1)^2=4p(y+3)\ \ \Rightarrow\ \ 4p=24\ \ \Rightarrow\ \  p=6\ \ \ and\ \ \ h=-1,\ k=-3\\\\the\ vertex:\ \ \ (h;\ k)=(-1;\ -3)\\\\the\ focus:\ \ \ (h;\ k+p)=(-1;\ -3+6)=(-1;\ 3)\\\\the\ directrix:\ \ \ y=k-p\ \ \ \Rightarrow\ \ \ y=-3-6=-9

You might be interested in
A plumber charges $130 2 hours of work and $235 for 5 hours of workWhat is the of change in dollars per hour
kogti [31]

Answer:

235

Step-by-step explanation:

Figure the rates per hr.

110/3 = 36 2/3

160/5 = 32.

So, the rates are not the same.

Knowing a bit about plumbers, they normally charge a basic fee to just show up, and then they charge per hr.

In cases like these, where we're asked to project to a new data point (in this case an 8-hr job), you should immediately think of a graph. The x-axis would be the hours worked. The y-axis would be the charge for the work (the cost of the job).

We're given two pairs of values:

(3,110) and (5,160).

The next step is to fit a line to them.

y = mx+b is the general equation for a line.

m = the slope = rise/run = change in y / change in x

Call the change in y, dy (for delta y).

Call the change in x, dx (for delta x).

m = dy/dx = 50/2 = 25

The slope is thus 25, which means for each hour, the price goes up by $25. That means the plumber charges $25/hr.

We also know the plumber charges $110 for a 3-hr job. 3*25 = $75. So the base charge would be $110-75 = $35.

y = 25x + 35

Checking this formula at x=3, we know it is 110.

Checking it at x=5, we obtain:

y = 25*5 + 35 = 125 + 35 = 160.

That checks.

Now to figure an 8-hr job, set x=8 and use the equation"

y = 25*8 + 35.

y = 200 + 35.

y = 235.

That means an 8-hr job costs $235.

3 0
3 years ago
Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1/3 c
True [87]
So we know there are 12 eggs and they will be distributed like this:

12=x2+y1
and 4 cups of flour:
4=1/3x+1/2y

let's see if we can find a solution in which all the materials are used:
12=x2+y1
4=1/3x+1/2y//*6

12=2x+y
24=2x+3y//*6

substract from each other:
12=2y
y=2
12=2x+y
12=2x+2
10=2x
x=5

So if nothing is wasted, he can make 5 blueberry muffins (making 12*5=60) and 2 bran muffins (2*9=18), together 78 dollars,

would it be better if instead of the bran muffins he did blueberry muffins (which are more expensive?)
for the branberry muffins he will used the double amount needed for 1: so 1 cup of oil and 2 eggs. From this he can only make 1 tray of blueberry muffins (and some oil will be left over), which will cost 12 dollars, which is less than 18

so he better make 6 blueberry and 2 bran trays






6 0
3 years ago
The graph of an absolute value function contains the points (1, 2), (0, 0), and (–1, 2). Shawn thinks the function this graph re
KATRIN_1 [288]

<span>In mathematics, the </span>absolute value<span> <span>or modulus. | x. | of a real number x is the non-negative </span></span>value<span> of x without regard to its sign. So both shawn and brielle are correct since both function will have the same answer, because it will just cancel out the sign.</span>

5 0
3 years ago
Read 2 more answers
If <br> 15=27<br> 12=21<br> 31=59<br> 24=45<br> then <br> 41=?
aleksley [76]

Answer:

41=79 41 is equal to 79.

3 0
3 years ago
Sum of two numbers is 24 and the difference is 15.What are the two numbers ?
natulia [17]
Translate that into an equation, and we get:

a+b = 24
a-b = 15

If we add these two equations, we get:

2a = 39
a = 39/2 = 19.5

Plug back in a = 19.5 and solve for b

a + b = 24
19.5 + b = 24
b = 4.5

The two numbers are 19.5 and 4.5.
4 0
3 years ago
Other questions:
  • What is the range? Please help
    6·1 answer
  • The bus driver made 6 stops on his way into town. No passengers left the bus. By stop 3, there were 9 passengers on the bus. How
    13·2 answers
  • Which method for calculating credit card balances is best for consumers who make large payments? A) Average daily balance method
    10·1 answer
  • HELP TEST DUE 12/1 The function f(x) = x − 1 is changed to f(x) = 1 4 x − 1. Which describes the effect of the change on the gra
    10·2 answers
  • Which of the following is NOT true
    11·1 answer
  • (x − 3)(2x2 − 5x + 1)
    8·1 answer
  • The length of the radius of a circle with an area of 100 yards is yards.
    6·1 answer
  • Plz help i'll give thanks and brainliest
    9·1 answer
  • 12.54 + (-24.673)<br><br><br> What’s the answer if you compute?
    12·1 answer
  • A gas tank on a car holds 16 gallons of gasoline and can travel 480 miles on a full tank. How many miles can the car travel usin
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!