A quadratic function y, equals, f, of, xy=f(x) is plotted on a graph and the vertex of the resulting parabola is left bracket, 3, comma, 4, right bracket(3,4). What is the vertex of the function defined as g, of, x, equals, f, of, x, minus, 3, plus, 2g(x)=f(x−3)+2?
To find the vertex of the function g(x) defined as g(x) = f(x-3) + 2, we need to shift the vertex of f(x) three units to the right and then stretch the parabola vertically by a factor of 2.
Given that the vertex of f(x) is at (3, 4), shifting it three units to the right gives us the new vertex at (6, 4). The vertical stretch by a factor of 2 means that the y-coordinate of the new vertex will be 2 times the original y-coordinate, so the new vertex for g(x) would be (6, 8).
Therefore, the vertex of the function g(x) = f(x-3) + 2 is (6, 8).