Let's find the y-intercept for the given quadratic function [tex]\( y = -4x^2 - 16x - 1 \)[/tex].
In general, the y-intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when [tex]\( x = 0 \)[/tex].
To find the y-intercept, substitute [tex]\( x = 0 \)[/tex] into the function:
1. Start with the given function:
[tex]\[
y = -4x^2 - 16x - 1
\][/tex]
2. Substitute [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -4(0)^2 - 16(0) - 1
\][/tex]
3. Simplify the equation:
[tex]\[
y = -4(0) - 16(0) - 1
\][/tex]
[tex]\[
y = 0 - 0 - 1
\][/tex]
[tex]\[
y = -1
\][/tex]
Therefore, the y-intercept of the quadratic function [tex]\( y = -4x^2 - 16x - 1 \)[/tex] is [tex]\( -1 \)[/tex].
So, the y-intercept is [tex]\( -1 \)[/tex].
