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
hjlf
3 years ago
11

What is the equation of the quadratic graph with a focus of (3,4) and a drirectrix of y =8

Mathematics
1 answer:
Pie3 years ago
8 0

check the picture below.  So the parabola looks more or less like so.


bearing in mind that the distance "p" is the same from the vertex to the directrix or the focus point, so the vertex is therefore half-way between those two fellows, now, from 3,4 up to y = 8, there are 4 units, and the vertex is half-way, thus is at y = 6, and x = 3, (3, 6) as you see there in the picture.

the parabola is vertical, meaning the squared variable is the "x", and is opening downwards, meaning the "p" distance is negative, so since "p" is 2 units, then p = -2.


\bf \textit{parabola vertex form with focus point distance}
\\\\
4p(y- k)=(x- h)^2
\qquad
\begin{array}{llll}
vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\begin{cases}
h=3\\
k=6\\
p=-2
\end{cases}\implies 4(-2)(y-6)=(x-3)^2\implies -8(y-6)=(x-3)^2
\\\\\\
y-6=\cfrac{(x-3)^2}{-8}\implies \blacktriangleright y=-\cfrac{1}{8}(x-3)^2+6 \blacktriangleleft

You might be interested in
PLEASE HELP!! SOON AS POSSIBLE.
Klio2033 [76]
2/15

90 ÷ 6 = 15

Theoretical probability would be 15 due to the equation above
7 0
3 years ago
Rafael graphed a line that contains the points (4, –6) and (–2, 6). What is the slope of the line that he graphed?
KIM [24]

Answer:

-2

Step-by-step explanation:

Your welcome!

6 0
3 years ago
Read 2 more answers
Solve the Quadratic Equation.
vichka [17]

Answer:

x = ± 2i

Step-by-step explanation:

The equation has no real roots, gut has complex roots

Given

x² = - 4 ( take the square root of both sides )

x = ± \sqrt{-4}

  = ± \sqrt{4(-1)}

[ Note that \sqrt{-1} = i ]

  = ± \sqrt{4} × \sqrt{-1} = ± 2i

7 0
3 years ago
If 3 is added to a number and the sum is tripled​, the result is 21 more than the number. find the number.
zavuch27 [327]
<span>If 3 is added to the number: x + 3
b) ...and the sum is tripled.. 
"The sum" is "x + 3" so: 3(x+3)
c) ...the result is 27 more than the number.
27 more than the number is x + 27 
d) Put it all together:
3(x + 3) = x + 27 
Solve for x: 
1) Distribute the left side of the equation:
3x + 9 = x + 27

2) Subtract x from each side of the equation:
2x + 9 = 27
3) Subtract 9 from each side of the equation:
2x = 18
4) Solve for x:
x = 9 
Check: 
1) x = 9
2) 3(x + 3) = x + 27
3) 3 ([9] + 3) = [9] + 27
4) 3(12) = 9 + 27
5) 36 = 36 

So, therefore The answer is correct</span>
7 0
3 years ago
Mr. Jackson rented a storage unit in the shape of a rectangular prism. The volume of the unit is 230 cubic yards. The storage un
attashe74 [19]

Answer:

4 yards

Step-by-step explanation:

the formula for finding the volume of a shape is volume= to length times with times how tall it is. In this case we do not have the hight so we make a formula. 5 and 3/4 times 10 times hight = to 230. If you do the math you get 4 yards as the answer.

8 0
3 years ago
Other questions:
  • Plz I don’t get this question your suppose to find the area
    13·1 answer
  • Line segments PQ and RS are parallel. Find the unknown length
    12·1 answer
  • Anyone else trying to study but t i k t o k is being addicting
    15·1 answer
  • Pls pls pls help!!!!!!
    12·1 answer
  • PLEASE HELP ME ASAP
    7·1 answer
  • Miguel made a circular flower garden with a diameter of 7 feet.
    5·1 answer
  • If Jan can buy 12 copies of a certain book for $40, what is the unit rate for cost per copy? How much
    14·1 answer
  • Write the equation for (-2,3) and (3,-1)
    12·1 answer
  • -3x + 3y = 9<br> 2x - 7y = -14
    12·1 answer
  • Comparing the two ratios 2/4 and 1/2<br> 2/4 is larger
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!