To identify the [tex]$y$[/tex]-intercept of the equation [tex]\( y = x^2 + 9 \)[/tex], we need to understand what a [tex]$y$[/tex]-intercept is. The [tex]$y$[/tex]-intercept is the point where the graph of the equation crosses the [tex]$y$[/tex]-axis. At this point, the value of [tex]$x$[/tex] is 0.
Here's a step-by-step solution:
1. Start with the given equation: [tex]\( y = x^2 + 9 \)[/tex].
2. Substitute [tex]\( x = 0 \)[/tex] into the equation to find the [tex]$y$[/tex]-intercept:
[tex]\[
y = (0)^2 + 9
\][/tex]
3. Calculate the value of [tex]\( y \)[/tex]:
[tex]\[
y = 0 + 9
\][/tex]
[tex]\[
y = 9
\][/tex]
4. Identify the [tex]$y$[/tex]-intercept: Since [tex]\( x = 0 \)[/tex] and [tex]\( y = 9 \)[/tex], the [tex]$y$[/tex]-intercept is at the point [tex]\( (0, 9) \)[/tex].
Therefore, the correct answer is:
D. [tex]\( (0, 9) \)[/tex]
