What is the inequality in factored form that describes the set of values that is greater than the quadratic function with zeros –12 and 3 and includes the boundary point (–4.5, –450).

A quadratic with zeros −12 and 3 has the form y = a(x + 12)(x − 3). Using the boundary point (−4.5, −450), we get −450 = a(7.5)(−7.5) = −56.25a, so a = 8. The function is y = 8(x + 12)(x − 3), and values greater than it are described by choice A. Strictly, the boundary point itself would be included by using ≥ rather than >.

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