We have been given that function [tex]g(x)=x^2+2[/tex] is a transformation of the quadratic parent function [tex]f(x)=x^2[/tex]. We are asked to find the y-intercept of function g.
We know that the function [tex]f(x)=x^2[/tex] is an upward opening parabola with vertex at point (0,0).
We know that vertex form of a parabola is in form [tex]y=a(x-h)^2+k[/tex], where point (h,k) represents vertex of parabola.
We can rewrite g(x) as:
[tex]g(x)=(x-0)^2+2[/tex]
The vertex of the function g(x) is at point (0,2).
We know that the vertex of a function is the point, when x is equal to 0. Therefore, the y-intercept of the g is at (0,2).
