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