Answer:
The equation is;
f(x) = -2·x² + 5·x - 1
Explanation:
The general form of a quadratic equation or function f(x) is, f(x) = y = a·x² + b·x + c
Given that the points representing the quadratic function are;
(-1, -8), (0, -1), (1, 2) which are of the form (x, y)
When x = -1, f(x) = y = -8
Plugging in the above values into the general form of a quadratic function, we have;
-8 = a·(-1)² + b·(-1) + c = a - b + c
-8 = a - b + c.........................(1)
When x = 0, y = -1, we have;
-1 = a·(0)² + b·(0) + c = c
c = -1.......................................(2)
When x = 1, y = 2, which gives;
2 = a·(1)² + b·(1) + c = a + b + c
2 = a + b + c........................(3)
Adding equation (1) to equation (3), we have;
-8 + 2 = a - b + c + a + b + c
-8 + 2 = 2·a + 2·c
From equation (2) c = -1, we get;
-8 + 2 = -6 = 2·a + 2·c = 2·a + 2 × (-1)
-6 = 2·a - 2
-4 = 2·a
a = -2
From equation (3), we have
2 = a + b + c
Substituting the values of a, and c gives;
2 = -2 + b - 1
b = 2 + 2 + 1 = 5
b = 5
The equation is therefore;
f(x) = -2·x² + 5·x - 1.