Question

Using the graph of f(x)=x^2 as a guide describe the transformations and then sketch a graph of each function. G(x)=(x-2)^2-7

Answer 1

we have

f(x)=x^2

Is a vertical parabola open upward

the vertex is a minimum

The vertex is the point (0,0)

g(x)=(x-2)^2-7

Is a vertical parabola open upward

the vertex is a minimum

The vertex is the point (2,-7)

the transformation of f(x) to g(x) has the following rule

(0,0) ------> (2, -7)

(x,y) ------> (x+2,y-7)

The translation is 2 units at right and 7 units down

using a graphing tool

see the attached figure

please wait a minute