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In this problem, we are tasked with determining the coefficients \(a\), \(b\), and \(c\) for the parabolic equation \(y = ax^2 + bx + c\), based on the three points \(A(1, 4)\), \(B(-2, -5)\), and \(C(3, 0)\). Here is a breakdown of the steps and tasks from the provided text:

### 1. **System of Equations:**
   To solve for \(a\), \(b\), and \(c\), we start by substituting the points into the parabolic equation \(y = ax^2 + bx + c\).
   
   - For \(A(1, 4

Determine the coefficients a, b, and c for the parabola y = ax^2 + bx + c given the points A(1,4), B(-2,-5), and C(3,0).

Solve for the coefficients of a quadratic equation y = ax^2 + bx + c using given points A(1,4), B(-2,-5), and C(3,0). The solution involves creating a system of linear equations and applying matrix inversion techniques.

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