On a coordinate plane, two parabolas open up. the solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). the dashed-line parabola, labeled g of x, goes through (3, 6), has a vertex at (5, 2), and goes through (7, 6). what is the equation of the translated function, g(x), if f(x) = x2? g(x) = (x + 5)2 + 2 g(x) = (x + 2)2 + 5 g(x) = (x – 2)2 + 5 g(x) = (x – 5)2 + 2

Option 4.

Step-by-step explanation:

The vertex form of a parabola is

                   ... (1)

where, a is a constant (h,k) is vertex.

The given function is

The vertex of the function is (0,0) and it goes through (-2, 4) and (2, 4).

It is given that the vertex of function g(x) is at (5,2).

Substitute h=5 and k=2 in equation.

g(x) is passes through (3, 6).

            .... (2)

Divide both sides by 4.

Substitute a=1 in equation (2).

The function g(x) is .

Therefor, the correct option is 4.

add an !

step-by-step explanation: