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
r-ruslan [8.4K]
3 years ago
7

Write an equation for a parabola that has a vertex (1, 2) and passes through the point (3, -6).

Mathematics
1 answer:
Alex3 years ago
6 0

Answer:

y= -2x²+4x.

Step-by-step explanation:

the common equation of the parabola is y=ax²+bx+c, where a, b, c - numbers.

1) the coordinates of the vertex are:

x_0=-\frac{b}{2a} \ and \ y_0=\frac{4ac-b^2}{4a}.

2) if according to the condition x₀=1, then b= -2a.

If according to the condition y₀=2, then   2=\frac{4ac-b^2}{4a}=\frac{4ac-4a^2}{4a}=c-a;

it means that c=a+2.

3) if b= -2a; c=a+2 and the point (3;-6) belongs to the given parabola, then it is possible to substitute them into the common equation of the parabola:

-6=3²*a-6a+a+2; ⇔ a= -2.

4) if a= -2, then b=-2a=4, and c=a+2=0.

5) if a=-2, b=4 and c=0, then the required equation of the parabola is:

y= -2x²+4x.

You might be interested in
Given a = 2i+j – 2k<br> b= -1 – 7j+k<br> Find a x b
castortr0y [4]

Step-by-step explanation:

a = 2i + j - k

b = -1 -7j + k

a × b = (2i + j - k) (-1 + 7j + k)

-2i + 14ij + 2ik - j + 7j^2 + jk + k -7jk - k^2

-2i + 14ij + 2ik -j +7j^2 +jk - 7jk + k - k^2

-2i + 14ij + 2ik - j +7j^2 - 6jk + k - k^2

7 0
3 years ago
EXPERTS/ACE/GENIUSES PLZ HELP
Anna71 [15]
I believe it's 8 because it's scale is 4 times bigger.
2×4=8
6 0
3 years ago
Read 2 more answers
3(-x - 4) = 3x + 5(x + 2)
Ket [755]
3(-x - 4) = 3x + 5(x + 2)
x=-2
7 0
3 years ago
Read 2 more answers
5. Find the product. 10 • –5 • –4 • 3 = ? (1 point) –600 –500 500 600
vladimir2022 [97]

Answer:

600

Step-by-step explanation:

10*-5=-50*-4=200*3=600

The answer is 600.

8 0
3 years ago
Read 2 more answers
Help i have no idea how to do this
Brums [2.3K]

Answer: 80

Step-by-step explanation: it is 80

6 0
2 years ago
Other questions:
  • Write x2 - 12x + 8 in vertex form. a. (x-6)2 -28 = 0 b. (x-4)2 - 11 = 0 c. (x-4)2 - 13 d. (x-4)2 - 15
    15·1 answer
  • What is the volume of a 3 foot tall cylindrical trash can with a 1 foot radius
    12·1 answer
  • (3+5)x7-[10+(45-15)\5]
    15·1 answer
  • SORRY I'M TO "SMART"!!! PLZ HELP!!!!
    9·2 answers
  • Please find mA and mB please.
    10·1 answer
  • 7.8%(54.99)+54.99=?<br>simplify the answer ​
    6·1 answer
  • It is given that x2 - 6x + 14 = (x+p) +9 Find the value of p and q.​
    7·1 answer
  • Here xchx solve this mate :)Thanks. 12 points smh
    8·1 answer
  • 3.52 in expanded form
    12·1 answer
  • 3x-1=5x+10. and the X= -5 1/2
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!