Problem

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

Answer

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Answer

Substituting this value back into the original equation gives us the final equation of the quadratic function: f(x)=−415(x+2)(x−6)

Steps

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=−415.

Step 6 ：Substituting this value back into the original equation gives us the final equation of the quadratic function: f(x)=−415(x+2)(x−6)

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