Question

describe the transformations that occur from the parent function f(x) = x2 to the function g(x) =2(x+1)^2-7

Answer 1

we have

f(x)=x^2

this is a vertical parabola with vertex at (0,0)

and

we have

g(x)=2(x+1)^2-7

this is a vertical parabola with vertex at (-1,-7)

so

the transformation of f(x) to g(x) is equal to

(0,0) ------> (-1,-7)

the rule of the translation is equal to

(x,y) --------> (x-1, y-7)

that means ------> the translation is 1 unit at left and 7 units down

and we have a second transformation

(x,y) -------> (ax, y)

the factor a is 2

therefore

First transformation

x^2 --------> 2x^2

second transformation

2x^2---------> 2(x+1)^2-7