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
Veseljchak [2.6K]
3 years ago
12

Find the equation of the parabola that passes through

Mathematics
1 answer:
valentinak56 [21]3 years ago
3 0

so we have the points of (0,-7),(7,-14),(-3,-19), let's plug those in the y = ax² + bx + c form, since we have three points, we'll plug each one once, thus a system of three variables, and then we'll solve it by substitution.

\bf \begin{array}{cccllll} \stackrel{\textit{point (0,-7)}}{-7=a(0)^2+b(0)+c}& \stackrel{point (7,-14)}{-14=a(7)^2+b(7)+c}& \stackrel{point (-3,-19)}{-19=a(-3)^2+b(-3)+c}\\\\ -7=c&-14=49a+7b+c&-19=9a-3b+c \end{array}

well, from the 1st  equation, we know what "c" is already, so let's just plug that in the 2nd equation and solve for "b".

\bf -14=49a+7b-7\implies -7=49a+7b\implies -7-49a=7b \\\\\\ \cfrac{-7-49a}{7}=b\implies \cfrac{-7}{7}-\cfrac{49a}{7}=b\implies -1-7a=b

well, now let's plug that "b" into our 3rd equation and solve for "a".

\bf -19=9a-3b-7\implies -12=9a-3b\implies -12=9a-3(-1-7a) \\\\\\ -12=9a+3+21a\implies -15=9a+21a\implies -15=30a \\\\\\ -\cfrac{15}{30}=a\implies \blacktriangleright -\cfrac{1}{2}=a \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{and since we know that}}{-1-7a=b}\implies -1-7\left( -\cfrac{1}{2} \right)=b\implies -1+\cfrac{7}{2}=b\implies \blacktriangleright \cfrac{5}{2}=b \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{2}x^2+\cfrac{5}{2}x-7~\hfill

You might be interested in
Which equation represents an exponential function that passes through the point (2, 36)?
Zepler [3.9K]

Answer:              It would be the first equation because:

Step-by-step explanation:        

In order to be an exponential function, the X

variable has to be in the exponent, that eliminates

the second and fourth answers

       f(X) = 4(3)X

using the point (2,36)

  f(2) = 4 (3)2

         = 4 (9 )

         = 36

6 0
2 years ago
Read 2 more answers
HELP PLEASEEEEEEE<br> 15 - 4x = 2(3x + 1)
bixtya [17]

Answer:

x = 1.3

Step-by-step explanation:

15 - 4x = 2(3x + 1)

15 - 4x = 6x + 2

-2                 -2

--------------------------

13 - 4x = 6x

   +4x      +4x

--------------------------

13 = 10x

/10    /10

---------------------------

1.3 = x

6 0
3 years ago
Read 2 more answers
Please HELP!!!!!
Stels [109]
Can you explain it more clear because my english is not very good, I want to easy to help you
3 0
3 years ago
What is the solution set of this system of equations?
Rina8888 [55]
D option is right answer
5 0
3 years ago
Read 2 more answers
Help pls will give brainliest
Dahasolnce [82]

Answer:

hello,

answer C

Step-by-step explanation:

area of the rectangle=2b*b=2b²

area of the half cercle= \\\dfrac{\pi*(\frac{c}{2})^2}{2} =\dfrac{\pi*c^2}{8} \\

Area in blue= 2b²-πc²/8

8 0
3 years ago
Other questions:
  • What is 5(-x) equal to?
    9·1 answer
  • n Pensacola, Florida, the average rainfall in the month of July is $7.40$ inches. By October, the average rainfall decreases by
    8·1 answer
  • Image is the question
    8·1 answer
  • Let the geometric sequence {an} be defined as follows: {12, 6, 3, 3 /2 , 3 /4 , 3/ 8 ,...} Find the sum of the entire sequence,
    12·1 answer
  • Which answer choice shows the numbers in order from greatest to least?
    7·2 answers
  • In the liner equation shown which variable represent the output values<br><br> Y= <br> MX + b
    15·1 answer
  • Reflection across the x-axis M(0,-1) S(3,2) Q(5,-3)
    8·1 answer
  • A. Download the printable diagram of the real number system. B. Find 10 numbers in the real world, with at least one number from
    13·1 answer
  • Given that B is the midpoint of segment AC. BC = 14x -26 and AB = 6x +6,<br> find the value of x.*
    15·1 answer
  • (PLEASE HELP)
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!