Answer:
Value of constant term c is (-4)
Explanation:
The given table represents a function which is in the form of a quadratic equation,
y = ax² + bx + c
We choose three points (3, -10), (4, -16) and (5, -24) from the table and satisfy the equation to get the values of a, b, and c.
For point (3, -10)
-10 = a(3)² + 3b + c
9a + 3b + c = -10 -------(1)
For point (4, -16)
-16 = a(4)² + 4b + c
16a + 4b + c = -16 ------(2)
For point (5, -24)
-24 = a(5)² + 5b + c
25a + 5b + c = -24 -----(3)
Equation (1) - equation (2)
(9a + 3b + c) - (16a + 4b + c) = -10 + 16
-7a - b = 6
7a + b = -6 ------(4)
Equation (2) - equation (3)
(16a + 4b + c) - (25a + 5b + c) = -16 + 24
-9a - b = 8
9a + b = -8 -------(5)
Equation (4) - Equation (5)
(7a + b) - (9a + b) = -6 + 8
-2a = 2
a = -1
From equation (4),
-7(1) + b = -6
b = -6 + 7
b = 1
From equation (1)
9(-1) + 3(1) + c = -10
-9 + 3 + c = -10
c = -10 + 6
c = -4
Therefore, the value of constant term c is (-4).