If `f(x)=a x^2+b x+c` is a quadratic function such that `f(1)=8,f(2)=11` and `f(-3)=6` find `f(x)` by using determinants. Also, find `f(0)dot`

Explanation

To solve the problem, we need to find the quadratic function \( f(x) = ax^2 + bx + c \) given the conditions \( f(1) = 8 \), \( f(2) = 11 \), and \( f(-3) = 6 \). We will use determinants to find the coefficients \( a \), \( b \), and \( c \).

### Step 1: Set up the equations

From the given conditions, we can set up the following equations:

1. \( f(1) = a(1)^2 + b(1) + c = 8 \)
This simplifies to:
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