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
Varvara68 [4.7K]
3 years ago
12

The equation for a parabola has the form y = ax^2 + bz + c, where a, b, and c are constants and aメ0. Find an equation for the pa

rabola that passes through the points (-1,14), (2,-7), and (5, 8) Answer: y-
Mathematics
1 answer:
vova2212 [387]3 years ago
5 0

Answer:

a = 2, b = -9, c = 3

Step-by-step explanation:

Replacing x, y values of the points in the equation y = a*x^2 + b*x +c give the following:  

(-1,14)

14 = a*(-1)^2 + b*(-1) + c  

(2,-7)

-7 = a*2^2 + b*2 + c  

(5, 8)  

8 = a*5^2 + b*5 + c  

Rearranging:

a - b + c = 14  

4*a + 2*b + c = -7

25*a + 5*b + c = 8

This is a linear system of equations with 3 equations and 3 unknows. In matrix notation the system is A*x = b whith:

A =

1    -1  1

4    2  1

25  5  1

x =

a  

b

c

b =

14

-7

8

Solving A*x = b gives x = Inv(A)*b, where Inv(A) is the inverse matrix of A. From calculation software (I used Excel) you get:

inv(A) =  

0.055555556 -0.111111111   0.055555556

-0.388888889 0.444444444   -0.055555556

0.555555556 0.555555556 -0.111111111

inv(A)*b

2

-9

3

So, a = 2, b = -9, c = 3

You might be interested in
Chin canned a number of quart jars and a number of pint jars of tomatoes from his garden. A pint is 16 ounces and a quart is 32
saveliy_v [14]
<span><span>Chin canned a number of quart jars and a number of pint jars of tomato. She canned total of 40 quarts, now what equation model did Chin used in the scenario 

let’s simplify the problem:
Pint = 16oz
quart = 32oz

what model best show to get 40quarts.
=> p + q = 40
=> 16p + 32q = 40

 the equation model that Chin used to get 40 quarts is p + q.</span></span><span> </span>
6 0
3 years ago
− 4 y − 3 + 3 y = 8 − 2 y − 15
Neporo4naja [7]

Answer:

y= -4

Step-by-step explanation:

simplify both sides of the equasion

add 2y to both sides

add three to both sides

and your answer is y= -4

7 0
3 years ago
List all the factors of the composite number 146
4vir4ik [10]
Factors: 1, 2, 73, 146.
4 0
2 years ago
Read 2 more answers
3) Differentiate with respect to x: a) (x²-3x+5)(2x-7)​
9966 [12]

Answer:

6x²-26x+31

Step-by-step explanation:

(x²-3x+5)(2x-7)​

=2x³-7x²-6x²+21x+10x-35

=2x³-13x²+31x-35

Now to differentiate:

dx=6x²-26x+31

4 0
2 years ago
Un producto que se venda en una tienda cuesta 85.000 y tiene un 15% de descuento. El nuvo precio, ¿a que porcentaje equivale en
Margaret [11]

Answer:

i dont speak that good in spanish but i can try

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Find the number 17% of which is 27 more than 14% of it.
    7·1 answer
  • Kevin is starting a saltwater aquarium with 36 fish. He wants to start with 11 times as many damselfish as clown fish. How many
    8·1 answer
  • Kara Danvers (Supergirl) has always relied on her strength to win fights. But what happens when she meets an alien just as stron
    8·1 answer
  • If a and −a are numbers on the number line, which expression MUST give the distance between them? A) 0 B) a Eliminate C) |2a| D)
    14·2 answers
  • Joshua has a bag of marbles. In the bag are 5 white marbles, 3 blue marbles, and 7 green marbles. Peter randomly draws one marbl
    13·1 answer
  • For each of the figures shown below, the existing coordinates are listed. Follow the instructions for each shape and perform the
    5·1 answer
  • If the area of a semicircle is 32 sq. km, then its radius is:
    14·1 answer
  • How to solve equations in which the variable is in an exponent
    13·1 answer
  • Shannon went bowling with her 2 friends. They paid $2 each to rent shoes and then $4.75 each for every game they bowled. If she
    9·1 answer
  • If m23 = 54°, find the measure of each missing angle.​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!