Question

Find a quadratic function to model the values in the table. Predict the value of y for x = 6.

x | y
-1 2
0 -2
3 10

Answer 1

Let the required quadratic equation be
y = ax^2 + bx + c
2 = a(-1)^2 + b(-1) + c
2 = a - b + c . . . (1)
-2 = a(0)^2 + b(0) + c
-2 = c . . . (2)
10 = a(3)^2 + b(3) + c
10 = 9a + 3b + c . . . (3)

Putting (2) into (1) and (3) gives
a - b - 2 = 2
a - b = 4 . . . (4)
9a + 3b - 2 = 10
9a + 3b = 12 . . . (5)

(4) * -3 => -3a + 3b = -12 . . . (6)
(5) - (6) => 12a = 24
a = 24/12 = 2.
From (4),
2 - b = 4
b = 2 - 4 = -2

Therefore, the required quadratic function is
y = 2x^2 - 2x - 2