Problem

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

Solution

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: \(\boxed{f(x) = -\frac{4}{15}(x+2)(x-6)}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8461/

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