Answer:
f(x) = 2x^2 - 4x + 8
Explanation:
To find an equation for the quadratic function represented by the table, we need to use the general form of a quadratic function:
f(x) = ax^2 + bx + c
where a, b, and c are constants to be determined.
Using the values from the table, we can set up a system of three equations to solve for a, b, and c:
(1) a(-1)^2 + b(-1) + c = 14
(2) a(0)^2 + b(0) + c = 8
(3) a(1)^2 + b(1) + c = 6
Simplifying each equation, we get:
(1) a - b + c = 14
(2) c = 8
(3) a + b + c = 6
Substituting equation (2) into equations (1) and (3), we get:
(1') a - b + 8 = 14
(3') a + b + 8 = 6
Simplifying equations (1') and (3'), we get:
(1'') a - b = 6
(3'') a + b = -2
Now we have two equations with two unknowns, which we can solve using elimination or substitution. For simplicity, we will use elimination:
Adding equations (1'') and (3''), we get:
2a = 4
Dividing both sides by 2, we get:
a = 2
Substituting a = 2 into equation (1''), we get:
2 - b = 6
Solving for b, we get:
b = -4
Substituting a = 2 and b = -4 into equation (2), we get:
c = 8
Therefore, the equation for the quadratic function represented by the table is:
f(x) = 2x^2 - 4x + 8