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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

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What is the difference of the fractions? Use the number line and equivalent fractions to help find the answer.
ipn [44]

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<h3>What is a number line?</h3>

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A sketch showing the representation of the difference in the mixed fractions can be seen in the image attached below.

Using equivalent expressions to determine the difference between the mixed fractions, we have;

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2 years ago
The ratio of black bags to blue bags is 5to 3 if there are a total of 10 black bags ,then how many blue bags are there
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Answer:

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