set up the systems of eqautions to solve for this quadratic function to model the values in the table

Answer :

The systems of equations to solve for this quadratic function to model the values in the table is y =  -2x^2 + 4x - 2

The general form of a quadratic function is --> y = ax2 + bx + c

-2 = a(0)2 + b(0) + c

-2 = 0 + 0 + c

-2 = c

substitute c value

(-1 , -8) substitute

-8 = a ( -1 )2 + b ( -1 ) - 2

-8 = a - b - 2

-6 = a - b

( 3 , -8)

-8 = a ( 3 )2 + b ( 3 ) - 2

-8 = 9a + 3b - 2

-6 = 9a + 3b

a - b = -6

9a + 3b = -6

on solving :

9 ( b - 6 ) + 3b = -6

9b - 54 + 3b = -6

12b - 54 = -6

12b = 48

b = 4

a - 4 = -6

a = -2

The quadratic equation for this table is y = -2x^2 + 4x - 2

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Full question:

set up the systems of eqautions to solve for this quadratic function to model the values in the table.

x | y

-1 | -8

0 | -2

3 | -8