Answer :
To find the y-intercept of a graph, you need to determine the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is equal to 0. The y-intercept is the point where the graph crosses the y-axis.
Let's find the y-intercept for the polynomial:
[tex]\[ y = -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108. \][/tex]
1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -0^6 - 6(0)^5 + 50(0)^3 + 45(0)^2 - 108(0) - 108. \][/tex]
2. Simplify each term:
[tex]\[
\begin{align*}
-0^6 & = 0, \\
-6(0)^5 & = 0, \\
50(0)^3 & = 0, \\
45(0)^2 & = 0, \\
-108(0) & = 0.
\end{align*}
\][/tex]
3. Add the constant term:
[tex]\[ y = 0 + 0 + 0 + 0 + 0 - 108 = -108. \][/tex]
Therefore, the y-intercept is at the point [tex]\((0, -108)\)[/tex].
The correct answer is B. [tex]\((0, -108)\)[/tex].
Let's find the y-intercept for the polynomial:
[tex]\[ y = -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108. \][/tex]
1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -0^6 - 6(0)^5 + 50(0)^3 + 45(0)^2 - 108(0) - 108. \][/tex]
2. Simplify each term:
[tex]\[
\begin{align*}
-0^6 & = 0, \\
-6(0)^5 & = 0, \\
50(0)^3 & = 0, \\
45(0)^2 & = 0, \\
-108(0) & = 0.
\end{align*}
\][/tex]
3. Add the constant term:
[tex]\[ y = 0 + 0 + 0 + 0 + 0 - 108 = -108. \][/tex]
Therefore, the y-intercept is at the point [tex]\((0, -108)\)[/tex].
The correct answer is B. [tex]\((0, -108)\)[/tex].
