Question 1209647
Here's how to determine f(-1):

1. **General form of a quadratic function:**

   f(x) = ax² + bx + c

2. **Set up a system of equations using the given information:**

   * f(1) = a(1)² + b(1) + c = a + b + c = -24
   * f(4) = a(4)² + b(4) + c = 16a + 4b + c = 10
   * f(3) = a(3)² + b(3) + c = 9a + 3b + c = 60

3. **Solve the system of equations:**

   There are several ways to solve this system. One approach is to use elimination or substitution. Here's one way:

   * Subtract the first equation from the second:
     15a + 3b = 34

   * Subtract the first equation from the third:
     8a + 2b = 84, which simplifies to 4a + b = 42

   * Solve for b in terms of a from the simplified third equation:
     b = 42 - 4a

   * Substitute this expression for b into the equation from subtracting the first two:
     15a + 3(42 - 4a) = 34
     15a + 126 - 12a = 34
     3a = -92
     a = -92/3

   * Substitute a back into the equation for b:
     b = 42 - 4(-92/3)
     b = 42 + 368/3
     b = (126 + 368)/3
     b = 494/3

   * Substitute a and b back into the first equation to solve for c:
     (-92/3) + (494/3) + c = -24
     402/3 + c = -24
     134 + c = -24
     c = -158

4. **Write the quadratic function:**

   f(x) = (-92/3)x² + (494/3)x - 158

5. **Calculate f(-1):**

   f(-1) = (-92/3)(-1)² + (494/3)(-1) - 158
   f(-1) = (-92/3) - (494/3) - 158
   f(-1) = -586/3 - 158
   f(-1) = -586/3 - 474/3
   f(-1) = -1060/3
   f(-1) = -353.3333...

Therefore, f(-1) = -1060/3 or approximately -353.33.