Answered

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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]

Sagot :

GinnyAnsweridn
To find the [tex]\( y \)[/tex]-intercept of the graph of the function [tex]\( f(x) = x^2 + 3x + 5 \)[/tex], we need to determine the point at which the graph intersects the [tex]\( y \)[/tex]-axis. The [tex]\( y \)[/tex]-intercept occurs when [tex]\( x = 0 \)[/tex].

Let's substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) \)[/tex]:

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

Simplify the right-hand side:

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

So, the [tex]\( y \)[/tex]-coordinate of the [tex]\( y \)[/tex]-intercept is 5. Therefore, the [tex]\( y \)[/tex]-intercept is the point [tex]\((0, 5)\)[/tex].

Thus, the answer is:
[tex]\((0, 5)\)[/tex]
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