The graph of a quadratic function has x-intercepts of -7 and -1, and passes through the point (-4,36). Determine the equation of the quadratic function in the form f(x) = a(x - m)(x − n).

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  f(x) = -4(x +7)(x +1)

Step-by-step explanation:

The x-intercepts tell us that m=-7 and n=-1. We can use the given point to find 'a'.

  f(-4) = 36

  a(-4+7)(-4+1) = 36

  a = 36/-9 = -4 . . . . divide by the coefficient of 'a'

Filling in the known values, ...

  f(x) = -4(x +7)(x +1)

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