graph the function

Question

graph g(x)=2(f)(x+1)-3 and

f(x)=2x^2+3 and explain how they relate

Answer 1

f(x+1)=2(x+1)^2+3=2(x^2+2x+1)+3=2x^2+4x+5. g(x)=2(2x^2+4x+5)-3=4x^2+8x+7.

The graphs are shown below in different colours: red is f(x); blue is f(x+1); green is g(x). Notice that the red and blue parabolas are the same size and shape; the green parabola is narrower then the others and all their vertices lie on the line y=3. Also, g(x) sits inside f(x+1) and shares the same vertex.