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
padilas [110]
3 years ago
11

What is the equation, in standard form, of a parabola that contains the following points?. . (–2, 18), (0, 2), (4, 42). . A) y =

–2x^2 – 2x – 3. B) y = –3x^2 + 2x – 2. C) y = 3x^2 – 2x + 2. D) y = –2x^2 + 3x + 3
Mathematics
2 answers:
Liula [17]3 years ago
6 0
Hello,
Answer C
y=ax²+bx+c 
(0,2)==>2=a*0²+b*0+c==>c=2

(4,42)==>42=a*16+4b+2==>4a+b=10 (1)
(-2,18)==>18=a*4-2*b+2==>4a-2b=16 (2)

(1)-(2) ==>3b=10-16 ==>b=-2
4a+(-2)=10==>4a=12==>a=3

y=3x²-2x+2 is the equation


3241004551 [841]3 years ago
5 0
<span>The equation of parabola is:
y = ax² + bx + c. 

</span>consider the (0, 2) to get the intercept.
substitute x = 0 and <span>y = 2 into the equation.
</span>2 = a(0)² + b(0) + c 
<span>c = 2 
</span>Similarly,
considering the point (- 2, 18): 
Substitute x = - 2 ,y = 18 ,and <span>c = 2 
</span>18 = a(- 2)² + b(- 2) + 2 
18 = 4a - 2b + 2 
Simplifying:
4a - 2b = 16 
<span>2a - b = 8 
</span>Solve for b:
Hence,
<span>b = 2a - 8 ------(1)
</span>
Now,
Substitute x = 4,y = 42, and c = 2
42 = a(4)² + b(4) + 2 
<span>42 = 16a + 4b + 2 </span>
<span>16a + 4b = 40 
</span>divide each term by 4.
We get,
<span>4a + b = 10 -------(2)
</span>
<span>Substitute b= 2a - 8 in Equation (2),
</span>We get:
4a + 2a - 8 = 10 
<span>6a = 18 + 8 </span>
<span>6a = 18 </span>
<span>a = 3 
</span>Substituting a = 3 in b=<span> 2a - 8
b = 6-8
b = -2
Hence,
our final equation will be:
</span><span>y = 3x² - 2x + 2</span>
You might be interested in
If a storm window has an area of 640 square inches, what is the equation to find the dimensions when the window is 20 inches hig
Strike441 [17]
<span>x(x-20)=640


Hope that helps!</span>
5 0
3 years ago
Please help what is the volume of the barn?
Naily [24]

Answer: 564

Step-by-step explanation:

10*14+40*10.6

Hoped this helped you have a blessed day and stay safe

7 0
4 years ago
A right triangle has one angle that measures 30°. What is the measure of the other acute angle?
Leto [7]

Answer:

60 degrees

Step-by-step explanation:

We know that a right triangle is 90 degrees

We have one angle given of 30 degrees

90 degrees - 30 degrees (known angle) = 60 degrees (unknown angle)

Therefore the unknown angle is 60

Please mark me brainliest

6 0
3 years ago
Martens got a small aquarium forgot her birthday. The aquarium is a right rectangular prism 18.5cm long by 15cm wide. Martens pu
sp2606 [1]

Answer:

Depth of Martens aquarium water = 14 cm.

Step-by-step explanation:

Given:

An aquarium,which is a right rectangular prism.

Length of the aquarium, l = 18.5 cm

Width of the aquarium, b = 15 cm

Volume of the aquarium, V = 3885 cm cubes

We have to find the depth of the aquarium.

Let the depth be h cm.

Note:

Volume of the rectangular prism,V=lbh.

⇒ V = l\times b\times h

⇒ h=\frac{V}{l\times b}

⇒ Plugging the values.

⇒ h=\frac{3885\ cm^3}{18.5\ cm\times 15\ cm}

⇒ h=14 cm

So,

The depth of the aquarium water is 14 cm.

4 0
4 years ago
3/4 is 60% of what number
kifflom [539]
3/4 is 60% of what number= 45

5 0
3 years ago
Read 2 more answers
Other questions:
  • A gardener purchases a ceramic planter, in the shape of a hemisphere, for a small batch of leftover annuals. The volume of a hem
    6·1 answer
  • PLEASE I NEED HELP IM FAILING AND I NEED TO GET MY GRADE UP
    12·1 answer
  • A graphing calculator is recommended. A grain silo consists of a cylindrical main section and a hemispherical roof. If the total
    11·1 answer
  • Can somebody help me with this due last week just haven’t been able to get to it
    7·1 answer
  • Solve 24 - 3 x = -27.
    9·1 answer
  • I need help solving this proportion!! <br><br> 3/x-1 = 2/x+4
    12·1 answer
  • What is the difference between 3 and 1/3
    5·1 answer
  • Please help, I’ll give brainliest UwU
    12·1 answer
  • Guy please help me out so this is the question 3.  Last Sunday, the temperature at 8:00 a.m. was -3०C.  Between 8:00 a.m and 1:0
    14·2 answers
  • The percentage of the battery's capacity that is charged as a function of time (in minutes) is graphed.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!