Question

A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (3,-5). What is the vertex of the function defined as g (x) =f(x-2)?

Answer 1

Shifting a quadratic function horizontally by \(h\) units to the right results in a new function with the vertex \((h+k, k)\), where \((h, k)\) is the original vertex.

In this case, the original vertex is \((3, -5)\), and you're shifting by \(h = 2\) units to the right. Therefore, the new vertex for \(g(x) = f(x-2)\) is \((3+2, -5) = (5, -5)\).