Let's find the missing values step-by-step.
The function given is [tex]\( f(x) = -(x+1)(x-3)(x+2) \)[/tex].
### Finding the Zeros
The zeros of the function are the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex].
To find the zeros, we need to set each factor equal to zero and solve for [tex]\( x \)[/tex]:
1. [tex]\( x + 1 = 0 \)[/tex]
[tex]\[
x = -1
\][/tex]
2. [tex]\( x - 3 = 0 \)[/tex]
[tex]\[
x = 3
\][/tex]
3. [tex]\( x + 2 = 0 \)[/tex]
[tex]\[
x = -2
\][/tex]
Thus, the zeros of the function [tex]\( f(x) \)[/tex] are [tex]\( -1, 3 \)[/tex], and [tex]\( -2 \)[/tex].
### Finding the Y-Intercept
The y-intercept of a function is the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex].
Substitute [tex]\( x = 0 \)[/tex] into the function and solve for [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = -( (0 + 1)(0 - 3)(0 + 2) )
\][/tex]
Simplify inside the parentheses first:
[tex]\[
f(0) = -( 1 \cdot -3 \cdot 2 )
\][/tex]
Then simplify further:
[tex]\[
f(0) = -(-6) = 6
\][/tex]
So, the y-intercept of the function is [tex]\( (0, 6) \)[/tex].
### Final Answer
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 y-intercept of the function is located at [tex]\( (0, 6) \)[/tex].
Thus, you should complete the boxes as follows:
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].
