Write a function to model the data.

x −3 −1 1 3 5
y −16 0 8 8 0

  f(x) = -(x +1)(x -5)

Step-by-step explanation:

The zeros at x = -1 and x = 5 tell us we can write this quadratic function as ...

  f(x) = a(x +1)(x -5)

for some scale factor "a".

When we put x=1 into the equation, we get ...

  f(1) = a(1+1)(1-4) = -8a

But we know that f(1) = 8, so ...

  8 = -8a

  -1 = a . . . . . . divide by -8

Now, we can write the function as ...

  f(x) = -(x +1)(x -5)

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If you like, you can expand this to ...

  f(x) = -(x^2 -4x -5)

  f(x) = -x^2 +4x +5 . . . . . "standard form"

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step-by-step explanation:

step-by-step explanation: