How would I sketch y=2(x-3)^2+12 In a graph?

The correct options are

(A) The x-value of a solution to the system of equations y = ƒ(x ) and y = g(x).

(C) The x-coordinate of an intersection point of the graphs of y = ƒ(x ) and y = g(x ).

Step-by-step explanation:  We are given to select the correct statements about the equation f(x) = g(x) from the given options.

Given functions are f(x) and g(x).

The solution of the equation f(x) = g(x) will be given by the values of 'x' which satisfy both the equations.

So,  the equation f(x) = g(x) will give the x-value of solution to the system of equations y = ƒ(x ) and y = g(x ).

Also, the solution of the equation is nothing but the x-coordinate of the point of intersection of both the functions.

Hence, the equation f(x) = g(x) will give the x-coordinate of intersection point of the graphs of y = ƒ(x ) and y = g(x ).

For example, let f(x) = x + 3  and  g(x) = 2x - 1.

Then,

And, when we draw the graphs of f(x) and g(x) as shown in the attached figure, x = 4 gives the x-coordinate of the point of intersection (4, 7).

Thus, the correct options are

(A) The x-value of a solution to the system of equations y = ƒ(x ) and y = g(x).

(C) The x-coordinate of an intersection point of the graphs of y = ƒ(x ) and y = g(x ).