determine the equation of a quadratic function with zeros -2 and 6 that passes through (1,4)

Step 1 ：The general form of a quadratic function is \(f(x) = a(x-h)(x-k)\), where h and k are the zeros of the function.

Step 2 ：In this case, h = -2 and k = 6.

Step 3 ：We also know that the function passes through the point (1,4), so we can substitute these values into the equation to solve for a.

Step 4 ：Substituting these values into the equation gives us \(eq = a*(x - 6)*(x + 2) - 4\).

Step 5 ：Solving this equation gives us a value of \(a = -\frac{4}{15}\).

Step 6 ：Substituting this value back into the original equation gives us the final equation of the quadratic function: \(\boxed{f(x) = -\frac{4}{15}(x+2)(x-6)}\)