<em>I know this is an older question, but for those who may come across this question, this is the answer I got.</em>
<em></em>
Answer:
The answer is $17.5.
Step-by-step explanation:
<em>c(x) = ax^(2) + bx + c</em>
c(3) = 15.5 = (equation)
- a(3)^2 + b(3) + c = 15.5
- (9a + 3b + c = 15.5)
c(7) = 23.5 = (equation)
- a(7)^2 + b(7) + c = 23.5
- (49a + 7b + c = 23.5)
c(12) = 56 = (equation)
- a(12)^2 + b(12) + c = 56
- (144a + 12b + c =56)
<u><em>The first two equations</em></u>
9a + 3b + c = 15.5 | x -1
+ 49a + 7b + c = 23.5
-9a - 3b - c =-15.5
+ 49a + 7b + c = 23.5
= 40a + 4b = 8/4
= 10a + b = 2
<u><em>The second and third equations</em></u>
49a + 7b + c = 23.5 | x -1
+ 144a + 12b + c = 56
-49a - 7b - c = -23.5
+ 144a + 12b + c = 56
= 95a + 5b = 32.5/5
= 19a + b = 6.5
<u><em>Now, we solve for a, b, and c</em></u>
10a + b = 2 | x -1
+ 19a + b = 6.5
-10a - b = -2
+ 19a + b = 6.5
= 9a = 4.5/9
= a = 0.5
10(0.5) + b = 2
5 + b = 2 | -5
= b = -3
49(0.5) + 7(-3) + c = 23.5
24.5 - 21 + c = 23.5
3.5 + c = 23.5 | -3.5
c = 20
<u><em>Then, plug it into the equation</em></u>
c(x) = 0.5x^2 - 3x + 20
c(x) = 0.5(5)^2 - 3(5) + 20
c(x) = 12.5 - 15 + 20
c(x) = 17.5
