Question

5
select the correct answer.
if function ( g(x) = x^2 + 2 ) is a transformation of the quadratic parent function, ( f(x) = x^2 ), where is the ( y )-intercept of function ( g ) located?
a. ( (0, -2) )
b. ( (2, 0) )
c. ( (0, 2) )
d. ( (-2, 0) )

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a function is the point where the graph of the function intersects the y - axis. At the y - axis, the x - coordinate is 0. So, to find the y - intercept of the function \(g(x)\), we need to substitute \(x = 0\) into the function \(g(x)\) and find the corresponding \(y\) - value.

Step2: Substitute \(x = 0\) into \(g(x)\)

Given the function \(g(x)=x^{2}+2\). When \(x = 0\), we have:
\(g(0)=(0)^{2}+2\)
First, calculate \((0)^{2}\), which is 0. Then, \(0 + 2=2\).

So, when \(x = 0\), \(y = 2\). The y - intercept is the point \((0,2)\).

Answer:

C. \((0,2)\)