To find the zeros of the function [tex]\( f(x) = -(x + 1)(x - 3)(x + 2) \)[/tex], we set [tex]\( f(x) = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[
-(x + 1)(x - 3)(x + 2) = 0
\][/tex]
Setting each factor to zero:
[tex]\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\][/tex]
[tex]\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\][/tex]
[tex]\[
x + 2 = 0 \quad \Rightarrow \quad x = -2
\][/tex]
Thus, the zeros of the function [tex]\( f(x) \)[/tex] are [tex]\(-1\)[/tex], [tex]\(3\)[/tex], and [tex]\(-2\)[/tex].
Next, to find the y-intercept, we evaluate the function at [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = -(0 + 1)(0 - 3)(0 + 2)
\][/tex]
[tex]\[
f(0) = -(1)(-3)(2)
\][/tex]
[tex]\[
f(0) = -(-6)
\][/tex]
[tex]\[
f(0) = 6
\][/tex]
Therefore, the y-intercept is located at [tex]\((0, 6)\)[/tex].
So, the completed statement is:
The zeros of the function [tex]\(f(x) = -(x + 1)(x - 3)(x + 2)\)[/tex] are [tex]\(-1, 3\)[/tex], and [tex]\(-2\)[/tex], and the [tex]\(y\)[/tex]-intercept of the function is located at [tex]\((0, 6)\)[/tex].
