Describe the transformation of f represented by g. Then graph each function. Describe the transformation of f represented by g. Then graph each function. f(x)=x^2; g(x)=3(x+2)^2-4

Answer 1

f(x) is an upward opening parabola with vertex at the origin

it's an even function symmetrical about x=1

its focus is (0,1/4), its directrix is y=-1/4

g(x) is f(x) shifted down 4, shifted left 2, and stretched vertically by a factor of 3

g(x) is an upward opening parabola, with vertex at (-2,-4), but "thinner" than f(x), it's an even function symmetrical about x=-2

its focus is (-2, -3 1/4) or (-2, -13/4) its directrix is y=- 4 3/4 =-19/4