To identify the [tex]\( y \)[/tex]-intercept of the quadratic function [tex]\( f(x) = -x^2 + 8x - 20 \)[/tex], we need to determine the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex]. The [tex]\( y \)[/tex]-intercept occurs where the graph of the function crosses the [tex]\( y \)[/tex]-axis, meaning at [tex]\( x = 0 \)[/tex].
Let's determine the [tex]\( y \)[/tex]-intercept step by step:
1. Given quadratic function:
[tex]\( f(x) = -x^2 + 8x - 20 \)[/tex]
2. Set [tex]\( x = 0 \)[/tex] to find the [tex]\( y \)[/tex]-intercept:
[tex]\( f(0) = -0^2 + 8(0) - 20 \)[/tex]
3. Simplify the expression:
[tex]\( f(0) = -0 + 0 - 20 \)[/tex]
[tex]\( f(0) = -20 \)[/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the quadratic function [tex]\( f(x) = -x^2 + 8x - 20 \)[/tex] is [tex]\( -20 \)[/tex]. This means the point at which the graph intersects the [tex]\( y \)[/tex]-axis is [tex]\((0, -20)\)[/tex].
