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The zeros of a function f(x) are 8 (double root) and -3 and the y-intercept is -768. Write the equation of f(x) in factored form.

Sagot :

sqdancefan

9514 1404 393

Answer:

  f(x) = -4(x +3)(x -8)²

Step-by-step explanation:

Each zero (z) gives rise to a factor (x -z). The given zeros mean the factored form is ...

  f(x) = a(x -8)²(x +3)

The value of this at x=0 is ...

  f(0) = a(-8)²(3) = 192a

We want the value to be -768, so ...

  -768 = 192a

  -4 = a . . . . . . . . divide by the coefficient of 'a'

Then the factored form is ...

  f(x) = -4(x +3)(x -8)²

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