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]
2 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:
Alex2 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
Surface area of a box dimensions of 16 18 and 14
Arada [10]
16×14×2+16×18×2+14×18×2=1528
3 0
3 years ago
Last year, the gym membership fee was $60. This year the fee is $48. By what percentage was the membership fee reduced​
dexar [7]
I think I went down by 29 dollars and 76 cent
5 0
3 years ago
A nursery has two hundred 7-gallon palm trees to sell, consisting of coconut palm trees, saw palmetto palm trees and christmas p
motikmotik

Total number of trees available to be sold = 200

Selling price of coconut palm trees sell (Pco)= $75 each

Selling price of saw palmetto palm trees sell (Pp) = $45 each

Selling price of christmas palm trees (Pch) = $30 each

Number of saw palmetto palm trees (Np) = 3 × Number of christmas palm trees (Nch)

Let number of coconut palm trees be Nco

Total price paid by developer for all the palm trees = 12,300

So Total number of trees = Nco + Np + Nch

⇒ 200 = Nco + 3×Nch + Nch

⇒ 200 = Nco + 4Nch ................ (i)

Total selling price of trees = Sco × Nco + Sp × Np + Sch × Nch

⇒ 12,300 = 75×Nco + 45×Np + 30×Nch

Dividing above equation by 5

⇒ 2,460 = 15Nco + 9Np + 6Nch

Substituting Np = 3Nch in the above equation

⇒ 2,460 = 15Nco + 9 (3Nch) + 6Nch

⇒ 2,460 = 15Nco + 33Nch ................ (ii)

Mutiply (i) with 15 and subtract from (ii)

⇒ 2,460 - 3,000 = 15Nco + 33Nch - 15Nco - 60Nch

⇒ -540 = 33Nch - 60Nch

⇒ -540 = 27Nch

⇒ Nch=20

If Nch = 20, Np = 3×20 = 60

Since Nco + Np + Nch = 200

⇒ Nco = 200 - (80)

⇒ Nco = 120

Hence, the developer purchased 120 coconut palm trees, 20 christmas palm trees and 60 saw palmetto palm trees.

6 0
3 years ago
How do u simplify the square root of 175
bekas [8.4K]
You could use a calculator or the best way to know is find a perfect square that multiplies another number to make that number. for example, square root of 175 (√175) = √25 times √7. then take the square root of the perfect square and multiply it by the square root. (√25 = 5) so the answer is 5 times √7. or 5√7
4 0
3 years ago
Does it mean when it saids "even"? Does absolute value mean even?​
Shkiper50 [21]

Answer:

Even is/means that the numbers add up to be even numbers.Also absolute Value mean is not even.

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • a map has a scale mileage chart with 100 miles equal to 1 inch. If a journey across part of Texas is 650 miles, how long is the
    5·1 answer
  • BRAINLIEST AWARD WILL BE GIVEN! PLEASE HELP WITH MATH IVE BEEN ASKING FOR HOURS! PLEASE ANYONE!!!
    14·1 answer
  • Mrs. Jennings had 5/7 gallons of paint. She gave 1/7 gallon each to some students. How many students received paint if Mrs. Jenn
    6·1 answer
  • What is 90000195 ×23982828728
    5·1 answer
  • How many solutions does this equation have 3x-2x+4=2+x+2
    8·1 answer
  • What is the value of 9x÷y³?
    10·1 answer
  • Can someone please help me it’s urgent
    11·2 answers
  • Answer it guys pls idk how... you can also show the steps. For those who answer it all correctly I will give the brainliest answ
    11·1 answer
  • A spinner has 10 sections numbered 1 to 10. Consider the events.
    7·1 answer
  • textRequest reports that adults 18–24 years old send and receive 128 texts every day. Suppose we take a sample of 25–34 year old
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!