What is the [tex]$y$[/tex]-intercept of the graph of the function [tex]$f(x) = x^2 + 3x + 5$[/tex]?

A. [tex]$(0, -5)$[/tex]
B. [tex]$(0, -3)$[/tex]
C. [tex]$(0, 3)$[/tex]
D. [tex]$(0, 5)$[/tex]



Answer :

To determine the [tex]$y$[/tex]-intercept of the function [tex]\( f(x) = x^2 + 3x + 5 \)[/tex], we need to find the value of the function when [tex]\( x = 0 \)[/tex].

The [tex]$y$[/tex]-intercept occurs where the graph of the function crosses the [tex]$y$[/tex]-axis. This happens when [tex]\( x = 0 \)[/tex].

Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) = x^2 + 3x + 5 \)[/tex]:

[tex]\[ f(0) = (0)^2 + 3(0) + 5 \][/tex]

Simplify the expression:

[tex]\[ f(0) = 0 + 0 + 5 = 5 \][/tex]

Therefore, the [tex]$y$[/tex]-intercept of the function is the point where [tex]\( x = 0 \)[/tex] and [tex]\( y = 5 \)[/tex]. Hence, the [tex]$y$[/tex]-intercept is [tex]\((0, 5)\)[/tex].

So, the correct answer is:

[tex]\[ (0, 5) \][/tex]