Answer:
The correct equation for g(x) is
[tex]B. g(x) = (x)^2 + 3[/tex]
Step-by-step explanation:
The given graph in the red represents the curve for the graph g(x).
Now as we observe: The graph cuts y - axis at (0,3)
⇒The value of graph g (x) = (0,3), when x = 0 and y = 3
or, the y - intercept of g(x) = 3
or, g(0) =3
Now, the given equation are:
[tex]A. g(x) = (x-3)^2\\\implies g(0) = (0-3)^2 = (3)^ 2 = 9 \neq 3\\[/tex]
or g(0) ≠ 3
So, A is NOT the required equation.
[tex]B. g(x) = (x)^2 + 3\\\implies g(0) = (0)^2 + 3= 0 + 3 = 3 = 3\\[/tex]
or g(0) = 3
So, B is the required equation.
[tex]C. g(x) = (x+3)^2\\\implies g(0) = (0+3)^2 = (3)^ 2 = 9 \neq 3\\[/tex]
or g(0) ≠ 3
So, C is NOT the required equation.
[tex]D. g(x) = (x)^2 - 3\\\implies g(0) = (0)^2 - 3 = 0 - 3 = -3 \neq 3\\[/tex]
or g(0) ≠ 3
So, D is NOT the required equation.
Hence, the correct equation for[tex]B. g(x) = (x)^2 + 3[/tex]
