Write a quadratic function f whose zeros are 7 and -5.

Answer:   f(x) = x² -2x -35Step-by-step explanation:You want a quadratic function that has zeros 7 and -5.FactorsEach zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).   f(x) = (x -7)(x +5)   f(x) = x² -2x -35__Additional commentYou may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.   sum: 7-5 = 2   product: (7)(-5) = -35   quadratic: f(x) = x² -2x -35