A quadratic function y = f ( x ) y=f(x) is plotted on a graph and the vertex of the resulting parabola is ( − 4 , − 6 ) (−4,−6). What is the vertex of the function g ( x ) = f ( x + 2 ) g(x)=f(x+2)?

Question

A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (−4,−6)(−4,−6). What is the vertex of the function defined as g(x)=f(x+2)g(x)=f(x+2)?

Answer 1

g(x) is f(x) shifted left 2 units

the vertex (-4,-6) is also shifted 2 units left

= (-4-2,-6) = (-6,-6)