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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 value of the function when [tex]\( x = 0 \)[/tex]. The [tex]\( y \)[/tex]-intercept is the point where the graph intersects the [tex]\( y \)[/tex]-axis, and this occurs when [tex]\( x = 0 \)[/tex].

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

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

Simplify the equation:

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

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

Therefore, the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = x^2 + 3x + 5 \)[/tex] is the point [tex]\( (0, 5) \)[/tex].

So, the correct answer is:

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