Question

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Answer 1

The correct equation for g(x) is

`B.  g(x) =  (x)^2 + 3`

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:

`A. g(x) = (x-3)^2\\\implies g(0) = (0-3)^2 = (3)^ 2  = 9 \\eq 3\\`

or g(0) ≠ 3

So, A is NOT the required equation.

`B. g(x) = (x)^2 + 3\\\implies g(0) = (0)^2  + 3= 0 + 3  = 3  = 3\\`

or g(0) = 3

So, B is the required equation.

`C. g(x) = (x+3)^2\\\implies g(0) = (0+3)^2 = (3)^ 2  = 9 \\eq 3\\`

or g(0) ≠ 3

So, C is NOT the required equation.

`D. g(x) = (x)^2 - 3\\\implies g(0) = (0)^2 - 3 = 0 - 3  = -3 \\eq 3\\`

or g(0) ≠ 3

So, D is NOT the required equation.

Hence, the correct equation for
`B.  g(x) =  (x)^2 + 3`