Answer:
Value of constant term c is (-4)
Step-by-step 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).
![\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &S&(~ -6 &,& 7~) % (c,d) &T&(~ -3 &,& 4~) \end{array}\\\\\\ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ ST=\sqrt{[-3-(-6)]^2+[4-7]^2}\implies ST=\sqrt{(-3+6)^2+(4-7)^2} \\\\\\ ST=\sqrt{3^2+(-3)^2}\implies ST=\sqrt{18}\implies ST=\sqrt{9\cdot 2} \\\\\\ ST=\sqrt{3^2\cdot 2}\implies ST=3\sqrt{2}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26S%26%28~%20-6%20%26%2C%26%207~%29%20%0A%25%20%20%28c%2Cd%29%0A%26T%26%28~%20-3%20%26%2C%26%204~%29%0A%5Cend%7Barray%7D%5C%5C%5C%5C%5C%5C%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B%5B-3-%28-6%29%5D%5E2%2B%5B4-7%5D%5E2%7D%5Cimplies%20ST%3D%5Csqrt%7B%28-3%2B6%29%5E2%2B%284-7%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B3%5E2%2B%28-3%29%5E2%7D%5Cimplies%20ST%3D%5Csqrt%7B18%7D%5Cimplies%20ST%3D%5Csqrt%7B9%5Ccdot%202%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B3%5E2%5Ccdot%202%7D%5Cimplies%20ST%3D3%5Csqrt%7B2%7D)
