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
Ket [755]
3 years ago
11

Part 4: Use the information provided to write the vertex formula of each parabola.

Mathematics
1 answer:
sergey [27]3 years ago
4 0

Answer:  1. x = (y - 2)² + 8

              \bold{2.\quad x=-\dfrac{1}{2}(y-10)^2}+1

               3. y = 2(x +9)² + 7

<u>Step-by-step explanation:</u>

Notes: Vertex form is: y =a(x - h)² + k    or      x =a(y - k)² + h

  • (h, k) is the vertex
  • point of vertex is midpoint of focus and directrix:   \dfrac{focus+directrix}{2}

     \bullet\quad a=\dfrac{1}{4p}

  • p is the distance from the vertex to the focus

1)

focus = \bigg(\dfrac{-31}{4},2\bigg)\qquad directrix: x=\dfrac{-33}{4}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{-31}{4}+\frac{-33}{4}}{2}=\dfrac{\frac{-64}{4}}{2}=\dfrac{-16}{2}=-8\\\\\text{The y-value of the vertex is given by the focus as: 2}\\\\\text{vertex (h, k)}=(-8,2)

Now let's find the a-value:

p=focus-vertex\\\\p=\dfrac{-31}{4}-\dfrac{-32}{4}=\dfrac{1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{4})}=\dfrac{1}{1}=1

Now, plug in a = 1   and    (h, k) = (-8, 2) into the equation x =a(y - k)² + h

x = (y - 2)² + 8

***************************************************************************************

2)

focus = \bigg(\dfrac{1}{2},10\bigg)\qquad directrix: x=\dfrac{3}{2}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1\\\\\text{The y-value of the vertex is given by the focus as: 10}\\\\\text{vertex (h, k)}=(1,10)

Now let's find the a-value:

p=focus-vertex\\\\p=\dfrac{1}{2}-\dfrac{2}{2}=\dfrac{-1}{2}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}

Now, plug in a = -1/2   and    (h, k) = (1, 10) into the equation x =a(y - k)² + h

\bold{x=-\dfrac{1}{2}(y-10)^2}+1

***************************************************************************************

3)

focus = \bigg(-9,\dfrac{57}{8}\bigg)\qquad directrix: y=\dfrac{55}{8}\\\\\text{Since directrix is y, then the y-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{57}{8}+\frac{55}{8}}{2}=\dfrac{\frac{112}{8}}{2}=\dfrac{14}{2}=7\\\\\text{The x-value of the vertex is given by the focus as: -9}\\\\\text{vertex (h, k)}=(-9,7)

Now let's find the a-value:

p=focus-vertex\\\\p=\dfrac{57}{8}-\dfrac{56}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2

Now, plug in a = 2   and    (h, k) = (-9, 7) into the equation y =a(x - h)² + k

y = 2(x +9)² + 7

You might be interested in
Can somebody answer this
Nimfa-mama [501]
A

Plug the values in and check


Mark brainliest please
4 0
3 years ago
Read 2 more answers
The length of a rectangle is four times its width.
MArishka [77]
Is the answer 240.is that one of your options
5 0
3 years ago
If two distinct planes intersect , then their intersection is a line . Which geometry term does the statement represent
Rom4ik [11]

Answer:

POSTULATE

Step-by-step explanation:

<em>A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven </em>

<em> </em>

<em>  </em>

<em> </em>

<em>In geometry, the theorem is considered valid or correct with which its assertion is practically not refuted by almost anyone, whether it is really true or not. </em>

<em> </em>

<em>  </em>

<em> </em>

<em>This, in practice, implies that all students of the subject share the same criteria on the theory. Thus, the postulates, in short, have the following characteristics: </em>

<em> </em>

<em>  They are presumed true by most of the scholars in the field. </em>

<em> </em>

<em>Its contradiction goes against the very essence of the subject. </em>

<em> </em>

<em>Postulate 6: If two planes intersect, then their intersection is a line.</em>

<em />

<em>See Attachment for Details ^^</em>

<em>The image attached  represents the statement given in the question (If two distinct planes intersect, then their intersection is a line)</em>

<em>Therefore</em><em>, </em>

<em> </em>

<em>The Geometry term that represents the statement above is POSTULATE</em>

5 0
3 years ago
Perimeter of an isosceles triangle is 90 m. If the length of the two equal sides is three fourth of the unequal side , find the
Sveta_85 [38]

Answer:

The length of the equal side is 27 meters each and that of the unequal side is 36 meters

Step-by-step explanation:

An isosceles triangle is a triangle with two sides being equal (also two equal base angles).

Let us assume the length of the two equal sides to be x meters each, and the length of the unequal side to be y meter. Since the perimeter of the triangle is 90 m, it can be expressed as:

x + x + y = 90

2x + y = 90

But the length of the equal side is  three fourth of the unequal side, i.e x = 3/4y

Therefore:

2(3/4y) + y = 90

3/2y + y = 90

2.5y = 90

y = 90/2.5

y = 36 meters

Also x = 3/4 * 36 = 27 meters

The length of the equal side is 27 meters each and that of the unequal side is 36 meters

5 0
3 years ago
According to the graph about _____ of households in Africa owns a computer in 2008.
inna [77]

Answer:

According to the graph about <u>5 percent</u> of households in Africa owns a computer in 2008.

2013 about 1/3 of all households in <u>Asia</u> had a computer.

The number of households with a computer is <u>increasing</u> in all regions overtime.

8 0
3 years ago
Other questions:
  • Out of 32 students in the class 5 said they rode their bikes to school based on their results how many of the 800 students in th
    14·1 answer
  • The number of hours you work in a week.​
    7·1 answer
  • Jennifer's teacher has marked this problem as one to recheck, but Jennifer cannot determine what she has done incorrectly. Ident
    7·1 answer
  • Solve the system of equations.<br> y = -6x + 9<br> y = -3x + 3
    9·1 answer
  • Factor completely: 4x2 + 25x + 6
    10·2 answers
  • Michael rents a car for one day. The charge is $30 plus the $0.12 per mile. He wants to spend exactly $105. How many miles can h
    12·1 answer
  • PLEASE HELP! I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLY! :)
    6·2 answers
  • Plz help I will give brainliest<br> What is the value of x in this problem<br> 97x+14=13.8
    6·1 answer
  • Please help me?
    14·1 answer
  • Which example is a nonrenewable energy source?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!