To find a quadratic function that models the given data points (0,77), (3,113), and (5,102), we can use the general form of a quadratic function:
f(x) = ax^2 + bx + c
Where a, b, and c are the coefficients we need to determine.
We can use the three data points to set up a system of three equations with three unknowns (a, b, and c):
f(0) = a(0)^2 + b(0) + c = c = 77
f(3) = a(3)^2 + b(3) + c = 9a + 3b + c = 113
f(5) = a(5)^2 + b(5) + c = 25a + 5b + c = 102
Solving this system of equations, we get:
a = -7/2
b = 45/2
c = 77
Therefore, the quadratic function that models the given data is:
[tex]f(x)= -3.5x^2 +22.5x + 77[/tex]