Which inequality is less than the quadratic function with zeros negative 7 and 1 and includes the point open paren 2 comma 27 halves close paren on the boundary?

A quadratic with zeros −7 and 1 has the form y = a(x + 7)(x − 1). Using the boundary point (2, 27/2), we get 27/2 = a(9)(1), so a = 3/2. Expanding gives y = (3/2)x² + 9x − 21/2, so the inequality is y < (3/2)x² + 9x − 21/2, choice C.

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