Question

Please answer this question

Answer 1

Answer:

y = $x^{2}$  - 2x - 3

Step-by-step explanation:

We know: y=ax^2+bx+c

Given:  (2, 5),  (3, 12), and (-1, -4)

so...

We plug in these numbers:

5 =  a*(2^2)  + b*2 + c

12 = a*(3^2)  + b*3  + c

-4 = a*((-1)^2) + b*(-1) + c

simplify:

5 = 4a + 2b + c

12 = 9a + 3b + c

-4 = a - b + c

Solve this 3 variable system

Combine   5 = 4a + 2b + c  and   -4 = a - b + c

-8 = 2a - 2b + 2c  from multiplying the equation -4 = a - b + c by 2

5 - 8 = 4a + 2a + 2b - 2b + c + 2c

-3 = 6a + 3c

-1 = 2a + c

next   multiply  -4 = a - b + c  by 3

-12 = 3a - 3b + 3c   add to 12 = 9a + 3b + c

-12 + 12 = 3a + 9a + -3b + 3b + 3c + c

0 = 12a + 4c

0 = 3a + c

combine   -1 = 2a + c and 0 = 3a + c

1 = -2a - c

0 + 1 =  3a - 2a + c - c

1 = a

so...  -1 = 2*1 + c

-1 = 2 + c

c = -1 -2 = -3

use equation  -4 = a - b + c ,  solve for b

-4 =  1 - b + (-3)

-4 = -2 - b

b = -2 + 4 = -2

so  a = 1, b = -2, c = -3

y = x^2  - 2x  - 3

y = $x^{2}$  - 2x - 3