To determine the location of the zeros of a quadratic function using the given table, we need to look for changes in the sign of f(x).
x
-2
-1
0
1
2
3
4
5
f(x)
6
1
-3
-5
-3
1
6
14
We see in the table that f(-1)=1, and that f(0)=-3. The function here goes from positive to negative. Therefore, there must be a zero between -1 and 0.
Similarly, look at f(2)=-3 and f(3)=1. Since the function here goes from negative to positive, there must be a zero between 2 and 3.
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