Answer:
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"
