Problem

2. A parabola has zeros at 4 and 6 and passes through the point $(8,-8)$. Determine the equation in factored form.

Answer

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Answer

Substituting the value of a back into the equation, we get the final equation: \(\boxed{y = -(x - 4)(x - 6)}\)

Steps

Step 1 ：Given that the parabola has zeros at 4 and 6, we can write its equation in factored form as: \(y = a(x - 4)(x - 6)\)

Step 2 ：Since the parabola passes through the point (8, -8), we can plug in the coordinates and solve for a: \(-8 = a(8 - 4)(8 - 6)\)

Step 3 ：Solving for a, we get: \(a = -1\)

Step 4 ：Substituting the value of a back into the equation, we get the final equation: \(\boxed{y = -(x - 4)(x - 6)}\)

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