To determine the [tex]\(y\)[/tex]-intercept of the graph of the polynomial function [tex]\( f(x) = -4x^2 + 3x - 1 \)[/tex], one needs to understand that the [tex]\( y \)[/tex]-intercept occurs where the graph crosses the [tex]\( y \)[/tex]-axis. At the [tex]\( y \)[/tex]-intercept, the value of [tex]\( x \)[/tex] is always [tex]\(0\)[/tex].
Given the polynomial function [tex]\( f(x) = -4x^2 + 3x - 1 \)[/tex], we can find the [tex]\( y \)[/tex]-intercept by substituting [tex]\( x \)[/tex] with [tex]\(0\)[/tex]:
[tex]\[ f(0) = -4(0)^2 + 3(0) - 1 \][/tex]
Solving this:
[tex]\[ f(0) = -4 \cdot 0 + 3 \cdot 0 - 1 \][/tex]
[tex]\[ f(0) = 0 + 0 - 1 \][/tex]
[tex]\[ f(0) = -1 \][/tex]
So, the [tex]\( y \)[/tex]-intercept of the graph is [tex]\((0, -1)\)[/tex].
Therefore, the correct answer is:
[tex]\[
(0, -1)
\][/tex]
