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If the function [tex]$g(x) = x^2 + 2$[/tex] is a transformation of the quadratic parent function [tex]$f(x) = x^2$[/tex], where is the [tex][tex]$y$[/tex][/tex]-intercept of function [tex]$g$[/tex] located?

A. [tex]$(0, -2)$[/tex]

B. [tex][tex]$(2, 0)$[/tex][/tex]

C. [tex]$(0, 2)$[/tex]

D. [tex]$(-2, 0)$[/tex]

Sagot :

GinnyAnsweridn
To determine the [tex]\( y \)[/tex]-intercept of the function [tex]\( g(x) = x^2 + 2 \)[/tex], we follow these steps:

1. Identify the point of interest: 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].

2. Substitute [tex]\( x = 0 \)[/tex] into the function: To find the [tex]\( y \)[/tex]-intercept, we evaluate the function [tex]\( g(x) \)[/tex] at [tex]\( x = 0 \)[/tex].

3. Calculate [tex]\( g(0) \)[/tex]:
[tex]\[ g(0) = 0^2 + 2 \][/tex]
[tex]\[ g(0) = 0 + 2 \][/tex]
[tex]\[ g(0) = 2 \][/tex]

4. Determine the coordinates of the [tex]\( y \)[/tex]-intercept: When [tex]\( x = 0 \)[/tex], [tex]\( g(x) = 2 \)[/tex]. Thus, the [tex]\( y \)[/tex]-intercept is at the point [tex]\((0, 2)\)[/tex].

Based on this, the correct answer is:
[tex]\[ \boxed{(0,2)} \][/tex]
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